孤子理论及其在玻色爱因斯坦凝聚中的应用
摘要
孤子理论是非线性科学的一个重要分支,它在物理学的许多领域中有着日益广泛的应用。孤子的微扰是孤子理论中最有实用价值的重要内容。它大体可以分为两大类。一是建立在逆散射变换基础上的孤子微扰理论。它在理论上有着重要的学术价值,但其思路较迂回曲折,数学计算较繁。另一种直接微扰沦较为系统的方法是将孤子方程线性化后再按Jost函数的平方作微扰展开。这两种方法均只适用于可积系统。近年来,颜家壬教授发展了一种基于分离变量法的孤子微扰理论法,它适用于可积和非可积系统,而且思路和计算较为简便。
在此,本文主要基于颜家壬教授的直接孤子微扰方法,通过改进,处理了扭结孤子的微扰问题。同时发展了孤子含时微扰理论。我们也应用这种系统的微扰方法处理了玻色-爱因斯坦凝聚中的孤子微扰问题。
玻色-爱因斯坦凝聚也是近几十年来被广泛关注的课题。它不仅提供了一个研究量子力学基本问题的宏观系统,也在原子激光,量子计算等领域有着重要的应用前景。玻色-爱因斯坦凝聚中的暗,亮物质波孤子的成功观测及它们的潜在的应用前景,也使玻色-爱因斯坦凝聚中的物质波孤子成为了当前低温物理和凝聚态物理研究领域的研究热点之一。本人主要是在平均场理论的框架下,以耦合Gross-Pitaevskii方程为主要模型,讨论了其中的多种孤子相互作用问题。
全文工作共分为两部分,主要内容如下:
第一部分为孤子理论方面,主要介绍三个工作。一、以扭结孤子为例,阐述对基于分离变量法的孤子微扰理论的方法改进。该方法主要是针对暗孤子微扰问题的解决而改进的。我们已用它处理了亮孤子,扭结孤子,暗孤子问题。在亮孤子和扭结孤子微扰问题处理中,发现它的结果与原方法所得结果一致,证明了其有效和正确性。二、基于颜家壬教授的直接微扰理论,我们发展了KdV孤子含时微扰理论。三、将孤子微扰理论由一阶扩展到二阶微扰,并用于一分量玻色-爱因斯坦凝聚中的孤子实际问题。我们所得结果,与前人用逆散射所得结果一致。但方法更清晰,计算更简单。
第二部分探讨两分量玻色-爱因斯坦凝聚中的孤子相互作用问题。主要介绍三个工作:一、耦合散焦非线性薛定谔方程中的孤子相互作用问题。从解析和数值模拟方面讨论了孤子之间的相对运动情况。二、对可调节的双种类玻色-爱因斯坦凝聚中的矢量孤子类型的分类,以及稳定性和相互作用情况的讨论。三、对可调节的双种类玻色-爱意斯坦凝聚中,可调种间相互作用,对亮亮孤子相互作用的影响的讨论。
最后对本文做了简单的总结和对我们所研究的领域前景的展望。我们的研究工作集中在三、四、六章。
Soliton theory is one of the important branches of nonlinear science.It has crescent application in many fields.The soliton perturbation problem is an important part of the soliton theory.It exists in a large number of real nonlinear systems and can be roughly divided into two kinds.One is based on the inverse scattering transformation(IST)which has important academic value.But this technique is inconvenient to those who are not familiar with IST.Another is the direct method where the squared Jost solutions are employed as the basis for perturbation expansion after soliton eqation been linearized.Both of them are just applicable tc integral systems.Professor Jiaren Yan,had developed a direct approach of the perturbation thoery based on separating variable technique,which is applicable to both integrable and unintegrable systems.It is more simple and convenient in method and calculation.
Here,We use an improved perturbation method,which is an improvement te a direct approach of perturbation theory for the nonlinear Schr(o|¨)dinger equation based on the separation of variables,to dispose the perturbation on kink solitons. At the same time,we developed the time-dependent perturbation thoery of soliton. Our method is also applied to dispose the soliton's perturbation problem in the system of the Bose-Einstein condensates.
Bose-Einstien condensates have been an attractive subjects in recent decades. They not only offer the perfect macrosciopic quantum systems to investigate many foundmental problems in quantum mechanics but also have extensively application foregrounds such as in atom laser and quantum computation.The observations of dark and bright matter wave solitons,the study of matter wave solitons have been one of the hot issues in the fields of both low-temperature physics and condensed matter physics due to their potential application.In the framework of mean-field theory,the Bose-Einstein condensates is govonered by the Gross-Pitaeviskii equation. Based on the coupled Gross-Pitaeviskii equation,we discuss the interaction between the vector solitons.
Our work is composed of two parts.The main contents as follows:
The fitst part,we give the study to the theory of the solitons.Three main works are introduced.Firstly,we take the perturbtions of the kink soliton as example, illustrate an improvement to a direct approach of perturbation theory for the nonlinear Schr(o|¨)dinger equation based on the separation of variables.This method is put forward for solving the perturbations of dark solitons.We had used it to deal with the perturbations of bright,kink,and dark solitons.We find the results is consistent with that of the primary method,and prove it's validity.Secondly,we developed the time-dependent perturbation theory of KdV soliton,which is also based on a direct approach of perturbation theory of Professor Yan Jiaren.At last,we extend this theory from the first-order perturbation to the second-order perturbation and give their applications on one-component Bose-Einstien condensates. Our results are accordant with that of the perturbation based on the inverse scattering transformation.But it is more simple and convenient in method and calculation.
The second part,we discuss the interaction between the solitons in two-componet Bose-Einstien condensates.We introduce three main works:The first work is the interaction between two bright solitons in coupled defocusing nonlinear Schr(o|¨)dinger equation.We discuss the relative motion of the two solitons from analytical analysis and numerical simulation.In the second work,we give categorys of vector solitons in dual-species Bose-Einstein condensates with an interspecies Feshbach resonance.We also discuss their stability and interaction.In the third work,we discuss the influence of the double species Bose-Einstein condensate with tunable interspecies interactions on the interaction of the bright vector solitons.
At last,we give a simple summary and discussion to the above-mentioned works.Here,our main works are involved in chapters three,four and six.
在此,本文主要基于颜家壬教授的直接孤子微扰方法,通过改进,处理了扭结孤子的微扰问题。同时发展了孤子含时微扰理论。我们也应用这种系统的微扰方法处理了玻色-爱因斯坦凝聚中的孤子微扰问题。
玻色-爱因斯坦凝聚也是近几十年来被广泛关注的课题。它不仅提供了一个研究量子力学基本问题的宏观系统,也在原子激光,量子计算等领域有着重要的应用前景。玻色-爱因斯坦凝聚中的暗,亮物质波孤子的成功观测及它们的潜在的应用前景,也使玻色-爱因斯坦凝聚中的物质波孤子成为了当前低温物理和凝聚态物理研究领域的研究热点之一。本人主要是在平均场理论的框架下,以耦合Gross-Pitaevskii方程为主要模型,讨论了其中的多种孤子相互作用问题。
全文工作共分为两部分,主要内容如下:
第一部分为孤子理论方面,主要介绍三个工作。一、以扭结孤子为例,阐述对基于分离变量法的孤子微扰理论的方法改进。该方法主要是针对暗孤子微扰问题的解决而改进的。我们已用它处理了亮孤子,扭结孤子,暗孤子问题。在亮孤子和扭结孤子微扰问题处理中,发现它的结果与原方法所得结果一致,证明了其有效和正确性。二、基于颜家壬教授的直接微扰理论,我们发展了KdV孤子含时微扰理论。三、将孤子微扰理论由一阶扩展到二阶微扰,并用于一分量玻色-爱因斯坦凝聚中的孤子实际问题。我们所得结果,与前人用逆散射所得结果一致。但方法更清晰,计算更简单。
第二部分探讨两分量玻色-爱因斯坦凝聚中的孤子相互作用问题。主要介绍三个工作:一、耦合散焦非线性薛定谔方程中的孤子相互作用问题。从解析和数值模拟方面讨论了孤子之间的相对运动情况。二、对可调节的双种类玻色-爱因斯坦凝聚中的矢量孤子类型的分类,以及稳定性和相互作用情况的讨论。三、对可调节的双种类玻色-爱意斯坦凝聚中,可调种间相互作用,对亮亮孤子相互作用的影响的讨论。
最后对本文做了简单的总结和对我们所研究的领域前景的展望。我们的研究工作集中在三、四、六章。
Soliton theory is one of the important branches of nonlinear science.It has crescent application in many fields.The soliton perturbation problem is an important part of the soliton theory.It exists in a large number of real nonlinear systems and can be roughly divided into two kinds.One is based on the inverse scattering transformation(IST)which has important academic value.But this technique is inconvenient to those who are not familiar with IST.Another is the direct method where the squared Jost solutions are employed as the basis for perturbation expansion after soliton eqation been linearized.Both of them are just applicable tc integral systems.Professor Jiaren Yan,had developed a direct approach of the perturbation thoery based on separating variable technique,which is applicable to both integrable and unintegrable systems.It is more simple and convenient in method and calculation.
Here,We use an improved perturbation method,which is an improvement te a direct approach of perturbation theory for the nonlinear Schr(o|¨)dinger equation based on the separation of variables,to dispose the perturbation on kink solitons. At the same time,we developed the time-dependent perturbation thoery of soliton. Our method is also applied to dispose the soliton's perturbation problem in the system of the Bose-Einstein condensates.
Bose-Einstien condensates have been an attractive subjects in recent decades. They not only offer the perfect macrosciopic quantum systems to investigate many foundmental problems in quantum mechanics but also have extensively application foregrounds such as in atom laser and quantum computation.The observations of dark and bright matter wave solitons,the study of matter wave solitons have been one of the hot issues in the fields of both low-temperature physics and condensed matter physics due to their potential application.In the framework of mean-field theory,the Bose-Einstein condensates is govonered by the Gross-Pitaeviskii equation. Based on the coupled Gross-Pitaeviskii equation,we discuss the interaction between the vector solitons.
Our work is composed of two parts.The main contents as follows:
The fitst part,we give the study to the theory of the solitons.Three main works are introduced.Firstly,we take the perturbtions of the kink soliton as example, illustrate an improvement to a direct approach of perturbation theory for the nonlinear Schr(o|¨)dinger equation based on the separation of variables.This method is put forward for solving the perturbations of dark solitons.We had used it to deal with the perturbations of bright,kink,and dark solitons.We find the results is consistent with that of the primary method,and prove it's validity.Secondly,we developed the time-dependent perturbation theory of KdV soliton,which is also based on a direct approach of perturbation theory of Professor Yan Jiaren.At last,we extend this theory from the first-order perturbation to the second-order perturbation and give their applications on one-component Bose-Einstien condensates. Our results are accordant with that of the perturbation based on the inverse scattering transformation.But it is more simple and convenient in method and calculation.
The second part,we discuss the interaction between the solitons in two-componet Bose-Einstien condensates.We introduce three main works:The first work is the interaction between two bright solitons in coupled defocusing nonlinear Schr(o|¨)dinger equation.We discuss the relative motion of the two solitons from analytical analysis and numerical simulation.In the second work,we give categorys of vector solitons in dual-species Bose-Einstein condensates with an interspecies Feshbach resonance.We also discuss their stability and interaction.In the third work,we discuss the influence of the double species Bose-Einstein condensate with tunable interspecies interactions on the interaction of the bright vector solitons.
At last,we give a simple summary and discussion to the above-mentioned works.Here,our main works are involved in chapters three,four and six.
引文
[1]Anthony J.Leggett.Bose-Einstein condensation in the alkali gases:some fundamental concepts.Rev.Mod.Phys.2001,73:307-354.
[2]S.N.Bose.Planck's law and light quantum hypothesis.Z.Phys.,1924,26:178-1711.
[3]A.Einstein.Quantentheorie des einatiomigen idealen Gases.Sitzungs-ber.Preuss.Akad.Wiss.,1924,1924:261.
[4]M.H.Anderson,J.R.Ensher,M.R.Matthews,C.E.Wieman,and E.A.Cornell.Observation of Bose-Einstein condensation in a dilute atomic vapor[j].Science,1995,269:198-201.
[5]K.B.Davis,M.O.Mewews,M.R.Andrews,N.J.van Druten,D.S.Durfee,D.M.Kurn,and W.Ketterle.Bose-Einstein condensation in a Gas of Sodium Atoms [J].Phys.Rev.Lett.,1995,75:3969-3973.
[6]C.C.Bradley,C.A.Sackett,J.J.Tollett,and R.G.Hulet.Evidence of Bose-Einstein Condensation in an Atomic Gas with Attractive Interactions[J].Phys.Rev.Lett.,1995,75:1687-1690.
[7]S.Burger,K.Bongs,S.Dettmer,W.Ertmer,K.Sengstock.Dark Solitons in Bose-Einstein Condensates[J].Phys.Rev.Lett.,1999,83:5198-5201.
[8]J.Denschlag,J.E.Simsarian,D.L.Feder,Charles W.Clark,L.A.Collins,J.Cubizolles,L.Deng,E.W.Hagley,K.Helmerson,W.P.Reinhardt,S.L.Rolston,B.I.Schneider,and W.D.Phillips.Generating Solitons by Phase Engineering of a Bose-Einstein Condensate[J].Science,2000,287:97-101.
[9]H.Saito and M.Ueda.Dynamically Stabilized Bright Solitons in a Two-Dimensional Bose-Einstein Condensate[J].Phys.Rev.Lett.,2003,90:040403.
[10]L.Khaykovich,F.Schreck,G.Ferrari,T.Bourdel,J.Cubizolles,L.D.Carr,Y.Castin,and C.Salomon.Formation of a Matter-Wave Bright Soliton[J].Science,2002,296:1290-1293.
[11]K.E.Strecker,G.B.Partridgel,A.G.Truscott,R.G.Hulet.Formation and propagation of matter-wave soliton trains[J].Nature,2002,417:150-153.
[12]Kaup D.J.A perturbation expansion for the Zakharov-Shabat inverse scattering transform[J].SIAM J.Appl.Math.,1976,31:121.
[13]Karpman V.I.Soliton evolution in the presence of perturbation[J].Phys.Scripta,1979,20:462.
[14]Maslov E.M.Second order perturbation theory for solitons[J].Teor.Mat.Fiz.,1980,42:362.
[15]Kivshar,Yu.S.and B.A.Malomed.Dynamics of solitons in nearly integrable systems [J].Rev.Mod.Phys.,1989,61:763.
[16]Gorshkov K.A.,and L.A.Ostrovsky.Interactions of solitons in nonintegrable systems:direct perturbation method and applications[J].Physica D,1981,428:1981.
[17]Ablowitz M.J,Clarkson P.A.Solitons,Nonlinear Evolution Equations and Inverse Scattering[M].London:Cambridge University Press,1991:149.
[18]Infled E,Rowlands G.Nonlinear Waves,Solitons and Chaos[M].England:Cambridge University Press,2000
[19]Rogers C,Schief W.K.B(a|¨)cklund and Darboux transformations geometry and mordern applications in soliton theory[M].UK:Cambridge University Press,Cambridge Texts in Applied Mathematics.2002.
[20]楼森岳,唐晓艳.非线性数学物理方法[M].北京:科学出版社,2006.
[21]Russell J.S.Report of the committee on waves.Rep.Meet,Brit.Assoc.Adv.Sci.7th Livepool,London,John Murray,1837:417.
[22]王明亮.非线性发展方程和孤立子[M].兰州:兰州大学出版社,1982.
[23]Zabusky N.J,Kruskal M.D.Interaction of “solitons” in a Collisionless Plasma and the Recurrence of Initial States[J].Phys.Rev.Lett.,1965,14:240.
[24]Haswgawa A,Tappert F.Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers[J].App.Phys.Lett,1973,23:142
[25]Gredeskul S.A,Kivshar Y.S.Generation of Dark Solitons in Optical Fiberslnteractions of solitons in nonintegrable systems:direct perturbation method[J].Phys.Rev.Lett,1989,62:977.
[26]Kumar A,Thomas Kurz,and Werner Lauterborn.Two-state bright solitons in doped fibers with saturating nonlinearity[J].Phys.Rev.E,1996,53:1166.
[27]A.Dreischuh,G.G.Paulus,F.Zacher,F.Grasbon,D.Neshev,and H.Walther.Modulational instability of multiple-charged optical vortex solitons under saturation of the nonlinearity[J].Phys.Rev.E,1999,60:7518.
[28]Carr L.D.Solitons in Bose-Einstein Condensates,doctor thesis,2001.
[29]Roberto Camassa and Darryl D.Holm.An integrable shallow water equation with peaked solitons[J].Phys.Rev.Lett.1993,71:1661-1664.
[30]S.Burger,K.Bongs,S.Dettmer,W.Ertmer,K.Sengstock,A.Sanpera,G.V.Shlyapnikov,and M.Lewenstein.Dark Solitons in Bose-Einstein Condensates[J].Phys.Rev.Lett,1999,83:5198.
[31]Jared C.Bronski,Lincoln D.Carr,Bernard Deconinck3,and J.Nathan Kutz.Bose-Einstein Condensates in Standing Waves:The Cubic Nonlinear Schrodinger Equation with a Periodic Potential[J].Phys.Rev.Lett,2001,86:1402-1405.
[32]Carr L.D,Clark C.W,and Reinhardt W.P.Stationary solutions of the one-dimensional nonlinear Schrodinger equation.I.Case of repulsive nonlinearity[J].Phys.Rev.A,2000,62:063610.
[33]C.S.Gardner,J.M.Greene,M.D.Kruskal and R.M.Miura.Method for solving the Korteweg-de Vries equation[J].Phys.Rev.Lett,1967,19:1095-1097.
[34]N.N.Huang.Theory of solitons and method of perturbation[M].Shanghai:Shanghai Scientific and Technological Education Publishing House,1996:1-99.
[35]R.Hirota.Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons[J].Phys.Rev.Lett,1971,27:1192-1194.
[36]刘式适和刘式达.物理学中的非线性方程[M].北京:北京大学出版社,2000:4-156.
[37]M.R.Miura.Backlund transformation[M].Berlin:Springer-Verlag,1978.
[38]C.Rogers and W.K.Shadwick.B(a|¨)cklund transformations and their applications [M].Academic Press,1982.
[39]M.L.Wang.Solitary wave solution for variant Boussineq equations[J].Phys.Lett.A.,1995,199:169-172.
[40]M.L.Wang.Exact solutions for a compound KdV-Burgers equation[J].Phys.Lett.A.,1996,213:279-287.
[41]M.L.Wang,Y.B.Zhou And Z.B.Li.Application of homogeneous balance method to exact solutions of nonlinear evolution equation in mathematical physics[J].Phys.Lett.A.,1996,216:67-75.
[42]E.G.Fan and H.Q.Zhang.New exact solutions to a system of coupled equations [J].Phys.Lett.A.,1998,245:389-392.
[43]D.J.Kaup.A perturbation expansion for the Zakharov-Shabat inverse scattering transform[J].SIAM J.Appl.Math.,1976,31:121-125.
[44]D.J.Kaup.Solitons as particles,oscillators,and in slowly changing media:a singular perturbation theory[J].Proc.R.Soc.A,1978,361:413-446.
[45]V.I.Karpman.Soliton evolution in the presence of perturbation[J].Phys.Scripta,1979,20:462-471.
[46]E.M.Maslov.Second order perturbation theory for solitons[J].Teor.Mat.Fiz.,1980,42:362-369.
[47]G.L.LAmb.Element of Soliton Theory[M].wiley:New York,1980:259-278
[48]Yu.S.Kivshar and B.A.Malomad.Dynamics of solitons in nearly integrable system[J].Rev.Mod.Phys.,1989,61:763-915.
[49]M.J.Ablowitz and P.A.Clarkson.Solitons,Nonlinear Evolution Equations and Inverse Scattering[M].England:Cambridge University Press,1991:31-38.
[50]V.M.Lashkin.Perturbation theory for dark solitons:Inverse scattering transform approach and radiative effects[J].Phys.Rev.E,2004,70:066620.
[51]K.A.Gorshkov and L.A.Ostrovskii.Interactions of solitons in non-integrable systems:direct perturbation method and applications[J].Physica D,1981,3(1):428-438.
[52]M.B.Fogel,S.E.Trullinger,A.R.Bishop and J.A.Krumhansl.Classical Particlelike Behavior of Sine-Gordon solitons in Scattering Potentials and Applied Fields[J].Phys.Rev.Lett.,1976,36:1411-1414.
[53]J.P.Keener and D.W.MClaughlin.Solitons under perturbations[J].Phys.Rev.A.,1977,16:777-790.
[54]R.L.Herman.A direct approach to studying soliton perturbation[J].J.Phys.A,1990,23:2327-2362
[55]V.V.Konotop and V.E.Vekslerchik.Direct perturbation theory for dark solitons [J].Phys.Rev.E,1994,49:2397-2407.
[56]X.J.Chen,Zh.D.Chen and N.N.Huang.Adirect perturbation theory for dark solitons based on a complete set of the squared Jost solutions[J].J.Phys.A,1998,31(2):6929-6947.
[57]J.R.Yan and Y.Tang.Direct approach to the study of soliton perturbation[J].Phys.Rev.E,1996,54:6816-6824.
[58]Y.Tang,J.R.Yah and Zh.H.Chen.Direct Approach for Kink Solution of φ-4Equation Under Perturbation[J].Chin.Phys.Lett,1997,14:845-848.
[59]J.R.Yah,Y.Tang and G.H.Zhou.Direct approach to the study of soliton perturbations of the nonlinear Schr(o|¨)dinger equation and the sine-Gordon equation[J].Phys.Rev.E,1998,58:1064-1073.
[60]F.Kh.Abdullaev,E.N.Tsoy,B.A.Malomed,and R.A.Kraenkel.Array of Bose-Einstein condensates under time-periodic Feshbach-resonance management [J].Phys.Rev.A,1998,68:053606.
[61]P.G.Kevrekidis,G.Theocharis,D.J.Frantzeskakis,and B.A.Malomed.Feshbach Resonance Management for Bose-Einstein Condensates[J].Phys.Rev.Lett.,2003,90:230401.
[62]G.Theocharis,P.Schmelcher,P.G.Kevrekidis,and D.J.Frantzeskakis.Matterwave solitons of collisionally inhomogeneous condensates[J].Phys.Rev.A,2005,72:033614
[63]Fatkhulla Kh.Abdullaev and Josselin Garnier.Propagation of matter-wave solitons in periodic and random nonlinear potentials[J].Phys.Rev.A,2005,72:061605(R)
[64]H.Sakaguchi and B.A.Malomed.Matter-wave solitons in nonlinear optical lattices [J].Phys.Rev.E,2005,72:046610.
[65]E.Ott and R.N.Sudan.Nonlinear theory of ion acoustic waves with Landau damping[J].Phys.Fluid.,1969,12:2388-2394
[66]K.Nozaki.Stochastic Instability of Sine-Gordon Solitons[J].Phys.Rev.Lett.,1982,49(26):1883-1885.
[67]B.A.Malomed and A.V.Ustinov.Pinning of a fluxion chain in a long Josephson Junction with a lattice of inhomogeneities:Theory and experiment[J].J.Appl.Phys.,1990,67:3791-3797
[68]D.J.Kaup.Thermal corrections to overdamped soliton motion[J].Phys.Rev.B,1983,27:6787-6795.
[69]D.J.Kaup.Perturbation theory for solitons in optical fibers[J].Phys.Rev.A,1990,42:5689-5694.
[70]D.J.Kaup.Second-order perturbations for solitons in optical fibers[J].Phys.Rev.A,1991,44(7):4582-4590
[71]M.B.Fogel,S.E.Trullinger,A.R.Bishop and J.A.Krumhansl.Dynamics of sine-Gordon solitons in the presence of perturbation[J].Phys.Rev.B,1977,15:1578-1592.
[72]J.R.Yan,Y.Tang and G.H.Zhou.First-order Correction of the perturbed Sine-Gordon Equation[J].Chin.Phys.Lett,1999,16:79-81
[73]J.R.Yan,Y.Tang and G.H.Zhou.Perturbation Theory for Nonlinear Klein-Gordon Kinks[J].Commun.Theor.Phys.,1999,32:375-382.
[74]J.R.Yan,L.X.Pan and G.H.Zhou.Soliton Perturbation for a Combined Kdv-MKdv Equation[J].Chin.Phys.Lett,2000,9:625-627.
[75]L.X.Pan,J.R.Yah and G.H.Zhou.Direct Approach for Soliton Perturbations Based on the Green's Function[J].Chin.Phys.,2001,7:594-598.
[76]Kaup,D.J.,J.Perturbation theory for solitons in optical fibers[J].Phys.Rev.A,1990,42:5689.
[77]Kaup D.J.Second-order perturbations for solitons in optical fibers.Phys.Rev.A,1991,44:4582.
[78]Herman R.J.A direct approach to studying soliton perturbations[J].J.Physics.A,1990,23:2327.
[79]Kivshar Y S and Malomed B A.Dynamics of solitons in nearly integrable systems.Rev.Mod.Phys.,1989,61:763.
[80]Li Zhi-Bin and Pan Su-Qi.广义五阶 KdV 方程的孤波解与孤子解[J].Acta Phys.Sin.,2001,50:402(in Chinese).
[81]Wei Cai-Min,Xia Zun-Quan and Tian Nai-Shuo.广义随机 KdV 方程新的精确类孤子解.Acta Phys.Sin.,2005,54:2463(in Chinese).
[82]S.N.Bose.Planck's law and light quantum hypothesis.Z.Phys.,1924,26:178-181.
[83]A.Einstein.Quantentheorie des einatomigen idealen Gases[J].Sitzungsber.Preuss.Akad.Wiss.,1924,1924:261.
[84]M.H.Anderson,J.R.Ensher,M.R.Matthews,C.E.Wieman,E.A.Cornell.Observation of Bose-Einstein condensation in a dilute atomic vapor[J].Science,1995,269:198-201.
[85]K.B.Davis,M.O.Mewes,M.R.Andrews,N.J.van Druten,D.S.Durfee,D.M.Kurn,and W.Ketterle.Bose-Einstein Condensation in a Gas of Sodium Atoms [J].Phys.Rev.Lett.,1995,75:3969-3973.
[86]C.C.Bradley,C.A.Sackett,J.J.Tollett,and R.G.Hulet.Evidence of Bose-Einstein Condensation in an Atomic Gas with Attractive Interactions.Phys.Rev.Lett.,1995,75:1687-1690.
[87]F.London.On the Bose-Einstein Condensation.Phys.Rev,1938,45:947-954.
[88]D.Hulin,A.Mysyrowicz,and C.Benoit Guillaume.Evidence for Bose-Einstein Statistics in an Exciton Gas.Phys.Rev.Lett.,1980,45:1970.
[89]J.L.Lin and J.P.Wolfe.Bose-Einstein condensation of paraexcitons in stressed Cu2O.Phys.Rev.Lett.,1993,71:1222.
[90]Jia Ling Lin and J.P.Wolfe.Bose-Einstein condensation of paraexcitons in stressed Cu_2O[J].Phys.Rev.Lett.,1993,71:1222-1225.
[91]C.J.Pethick and H.Smith.Bose-Einstein condensation in Dilute gases[M].Uk:Cambrige University Press,2002.
[92]D.J.Wineland,R.E.Drullinger,and F.L.Walls.Radiation-Pressure Cooling of Bound Resonant Absorbers[J].Phys.Rev.Lett.,1978,40:1639-1642.
[93]W.D.Phillips,H.Metcalf.Laser Deceleration of an Atomic Beam[J].Phys.Rev.Lett.,1982,48:596-599.
[94]D.G.Fried et al.Bose-Einstein Condensation of Atomic Hydrogen[J].Phys.Rev.Lett.,1998,81:3811-3814.
[95]S.Cornish,N.Claussen,J.Roberts,E.Cornell,C.Wieman.Stable 85Rb Bose-Einstein Condensates with Widely Tunable Interactions[J].Phys.Rev.Lett.,2000,85:1795-1798.
[96]G.Modugno,G.Ferrari,G.Roati,R.J.Brecha,A.Simoni,and M.Inguscio.Bose-Einstein Condensation of Potassium Atoms by Sympathetic Cooling[J].Science,2001,294:1320-1322.
[97]A.Robert,O.Sirjean,A.Browaeys,J.Poupard,S.Nowak,D.Boiron,C.I.Westbrook,and A.Aspect.A Bose-Einstein Condensate of Metastable Atoms[J].Science,2001,292:461-464.
[98]T.Weber et al.Bose-Einstein Condensation of Cesium[J].Science,2002,299:232-235.
[99]Yosuke Takasu,Kenichi Maki,Kaduki Komori,Tetsushi Takano,Kazuhito Honda,Mitsutaka Kumakura,Tsutomu Yabuzaki,and Yoshiro Takahashi.Spin-Singlet Bose-Einstein Condensation of Two-Electron Atoms[J].Phys.Rev.Lett.,2003,91:040404(4).
[100]T.Radu,H.Wilhelm,V.Yushankhai,D.Kovrizhin,R.Coldea,Z.Tylczynski,T.L(u|¨)hmann,and F.Steglich.Bose-Einstein Condensation of Magnons in Cs_2CuCl_4[J].Phys.Rev.Lett.,2005,95:127202(4).
[101]周蜀渝,龙全,周善钰,付海翔,王育竹.玻色-爱因斯坦凝聚在中国科学院上海光机所实现[J].物理,2002,31:481-482.
[102]F.Dalfovo,S.Giorgini,L.P.Pitaevskii,and S.Stringari.Theory of Bose-Einstein condensation in trapped gases[J].Rev.Mod.Phys.1999,71:463-512.
[103]A.J.Leggett.Bose-Einstein condensation in the alkali gases:Some fundamental concepts[J].Rev.Mod.Phys.,2001,73:307-356.
[104]C.J.Myatt,E.A.Burt,R.W.Ghrist,E.A.Cornell,C.E.Wieman.Production of Two Overlapping Bose-Einstein Condensates by Sympathetic Cooling[J].Phys.Rev.Lett.,1997,78,586.
[105]G.Modugno,M.Modugno,F.Riboli,G.Roati,M.Inguscio.Two Atomic Species Superfluid[J].Phys.Rev.Lett.,2002,89:190404.
[106]G.D.Telles,A.R.L.Caires,V.S.Bagnato,L.G.Marcassa.Observation of Ultracold Ground-State Heteronuclear Molecules[J].Phys.Rev.Lett.,2004,92:133203.
[107]S.B.Papp,C.E.Wieman.Observation of Heteronuclear Feshbach Molecules from a~(85)Rb-~(87)Rb Gas[J].Phys.Rev.Lett.,2006,97:180404.
[108]M.Modugno,F.Ferlaino,F.Riboli,G.Roati,G.Modugno.M.Inguscio.Meanfield analysis of the stability of a K-Rb Fermi-Bose mixture[J].Phys.Rev.A 2003,68:043626;C.Ospelkaus,S.Ospelkaus,L.Humbert,P.Ernst,K.Sengstock,K.Bongs.Ultracold Heteronuclear Molecules in a 3D Optical Lattice[J].Phys.Rev.Lett.,2006,97:120402
[109]D.M.Stamper-Kurn,M.R.Andrews,A.P.Chikkatur,S.Inouye,H.-J.Miesner,J.Stenger,and W.Ketterle,Optical Confinement of a Bose-Einstein Condensate,Phys.Rev.Lett.1998,80:2027-2030.
[110]M.D.Barrett,J.A.Sauer,and M.S.Chapman.All-Optical Formation of an Atomic Bose-Einstein Condensate[J].Phys.Rev.Lett.2001,87:010404(4).
[111]M.-S.Chang,C.D.Hamley,M.D.Barrett,J.A.Sauer,K.M.Fortier,W.Zhang,L.You,and M.S.Chapman.Observation of Spinor Dynamics in Optically Trapped ~(87)Rb Bose-Einstein Condensates[J].Phys.Rev.Lett.,2004,92:140403(4).
[112]P.Maddaloni,M.Modugno,C.Fort,F.Minardi,and M.Inguscio.Collective Oscillations of Two Colliding Bose-Einstein Condensates[J].Phys.Rev.Lett.,2000,85:2413-2417.
[113]C.J.Myatt,E.A.Burt,R.W.Ghrist,E.A.Cornell,and C.E.Wieman.Production of Two Overlapping Bose-Einstein Condensates by Sympathetic Cooling [J].Phys.Rev.Lett.,1997,78:586-589.
[114]D.S.Hall,M.R.Matthews,J.R.Ensher,C.E.Wieman,and E.A.Cornell.Dynamics of Component Separation in a Binary Mixture of Bose-Einstein Condensates [J].Phys.Rev.Lett.,1998,81:4531-4534.
[115]J.Williams,R.Walser,J.Cooper,E.Cornell,and M.Holland.Nonlinear Josephson-type oscillations of a driven,two-component Bose-Einstein condensate [J].Phys.Rev.A,1999,59:R31-R34.
[116]S.Inouye,M.R.Andrews,J.Stenger,H.J.Miesner,D.M.Stamper-Kurn,and W.Ketterle.Observation of Feshbach resonances in a Bose-Einstein condensate[J].Nature,1998,392:151-154.
[117]Markus Grelner,01af Mandel,Tllman Essllnger,Theodor W.Hansch,Immanuel Bloch.Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms[J].Natue,2002,415:39-44.
[118]Th.Busch and J.Anglin.Dark-Bright Solitons in Inhomogeneous Bose-Einstein Condensates[J].Phys.Rev.Lett,2001,87(1):010401.
[119]A.D.Jackson,G.M.Kavoulakis,and C.J.Pethick.Solitary waves in clouds of Bose-Einstein condensed atoms[J].Phys.Rev.A,1998,58(3):2417-2422.
[120]L.D.Carr,Charles W.Clark,and W.P.Reinhardt.Stationary solutions of the one-dimensional nonlinear Schrodinger equation.I.Case of repulsive nonlinearity[J].Phys.Rev.A,2000,62(6):063610.
[121]L.D.Carr,J.Brand,S.Burger et al.Dark-soliton creation in Bose-Einstein condensates[J].Phys.Rev.A,2001,63(5):051601.
[122]J.Dziarmaga and K.Sacha.Depletion of the dark soliton:The anomalous mode of the Bogoliubov theory[J].Phys.Rev.A,2002,66:043620.
[123]R.Dum,J.I.Cirac,M.Lewenstein,et al.Creation of Dark Solitons and Vortices in Bose-Einstein Condensates[J].Phys.Rev.Lett,1998,80(14):2972-2975.
[124]S.Burger,L.D.Carr,P.berg et al.Generation and interaction of solitons in Bose-Einstein condensates[J].Phys.Rev.A,2002,65:043611.
[125]D.J.Frantzeskakis,G.Theocharis,F.K.Diakonos,et al.Interaction of dark solitons with localized impurities in Bose-Einstein condensates[J].Phys.Rev.A,2002,66:053608.
[126]W.P.Zhang,D.F.Walls and B.C.Sanders.Atomic soliton in a traveling wave laser beam[J].Phys.Rev.Lett,1994,72(1):60-63.
[127]B.Wu,J.Liu and Q.Niu.Controlled Generation of Dark Solitons with Phase Imprinting[J].Phys.Rev.Lett,2002,88:034101.
[128]T.Hong,Y.Z.Wang,and Y.S.Huo.Temporal dark solitons in nonuniform Bose-Einstein condensates[J].Phys.Rev.A,1998,58(4):3128-3133.
[129]G.Huang,V.A.Makarov and M.G.Velarde.Two-dimensional solitons in Bose-Einstein condensates with a disk-shaped trap[J].Phys.Rev.A,2003,67:023604.
[130]G.Huang,Jacob Szefte and Shanhua Zhu.Dynamics of dark solitons in quasione-dimensional Bose-Einstein condensates[J].Phys.Rev.A,2002,65:053605.
[131]U.A.Khawaja,H.T.C.Stoof,R.G.Hulet,K.E.Strecker and G.B.Partridge.Bright Soliton Trains of Trapped Bose-Einstein Condensates[J].Phys.Rev.Lett.,2002,89:200404.
[132]V.Y.F.Leung,A.G.Truscott,K.G.H.Baldwin et al.Nonlinear atom optics with bright matter-wave soliton trains[J]Phys.Rev.A,2002,66:061602.
[133]L.D.Carr,Y.Castin Dynamics of a matter-wave bright soliton in an expulsive potential[J].Phys.Rev.A,2002,66:063602.
[134]U.Al.Khawajia,H.T.C.Stoof,R.G.Hulet,K.E.Strecker,and G.B.Partridge Bright Soliton Trains of Trapped Bose-Einstein condensates[J]Phys.Rev.Lett.,2002,89:200404.
[135]V.M.P(?)rez-Garc(?)a,H.Michinel,H.Herrero.Bose-Einstein solitons in highly asymmetric traps[J].Phys.Rev.A,1998,57:3837-3842.
[136]W.Hai,S.Huang and K.Gao.Wavepacket trains of a Paul trapped ion[J].J.Phys.B,2003,36:3055-3061.
[137]F.Kh.Abdullaev,and R.Galimzyanov.The dynamics of bright matter wave solitons in a quasi one-dimensional Bose-Einstein condensate with a rapidly varying trap[J].J.Phys.B,2003,36:1099-1108.
[138]H.Satio,and M.Ueda.Dynamically Stabilized Bright Solitons in a Two-Dimensional Bose-Einstein condensate[J].Phys.Rev.Lett.,2003,90:040403.
[139]M.R.Andrews,D.M.Kurn,H.J.Miesner,D.S.Durfee,C.G.Townsend,S.Inouye and W.Ketterle.Propagation of Sound in a Bose-Einstein condensate[J].Phys.Rev.Lett.,1997,79:553-556.
[140]F.Dalfovo and Stefano Giorgini.Theory of Bose-Einstein condensation in trapped gases[J].Rev.Mod.Phys.,1999,71(3):463-512.
[141]张礼,葛墨林.量子力学的前沿问题[M],北京:清华大学出版社,2000.
[142]S.Burger,K.Bongs,S.Dettmer,W.Ertmer,K.Sengstock,A.Sanpera,G.V.Shlyapnikov,and M.Lewenstein.Darl solitons in Bose-Einstein Condensates[J].Phys.Rev.Lett.,1999 83:5198.
[143]J.Denschlag,J.E.Simsarian,D.L.Feder,C.W.Clark,L.A.Collins,J.Cubizolles,L.Deng,E.W.Hagley,K.Helmerson,W.P.Reinhardt,S.L.Rolston,B.I.Schneider,W.D.Phillips.Generating Solitons by Phase Engineering of a Bose-Einstein Condensete[J].Science 2000,287:97.
[144]L.Dobrek,M.Gajda,M.Lewenstein,K.Sengstock,G.Birkl,W.Ertmer.Optical generation of vortices in trapped Bose-Einstein condensates[J].Phys.Rev.A,1999,60:R3381.
[145]S.Burger,L.D.Carr,P.Ohberg,K.Sengstock,A.Sanpera.Generation and interaction of solitons in Bose-Einstein condensates[J].Phys.Rev.A,2002,65:043611.
[146]H.Saito and M.Ueda.Dynamically Stabilized Bright Solitons in a Two-Dimensional Bose-Einstein Condensate[J].Phys.Rev.Lett.,2003,90:040403.
[147]L.Khaykovich,F.Schreck,G.Ferrari,T.Bourdel,J.Cubizolles,L.D.carr,Y.Castin,C.Salomon.Formation of a Matter-Wave Bright solion[J].Science 2002,296:1290-1293
[148]K.E.Strcker,G.B.Partridge,A.G.Truscott,R.G.Hulet.Formation and propagation of the matter-wave soliton trains[J].Nature,2002,417:150-153.
[149]Z.X.Liang,Z.D.Zhang,and W.M.Liu.Dynamics of a Bright Soliton in Bose-Einstein Condensates with Time-Dependent Atomic Scattering Length in an Expulsive Parabolic Potential[J].Phys.Rev.Lett.,2005,94:050402(4).
[150]P.J.Y.Louisl,E.A.Ostrovskaya,C.M.Savage,and Y.S.Kivshar.Bose-Einstein condensates in optical lattices:Band-gap structure and solitons[J].Phys.Rev.A,2003,67:013602.
[151]B.Eiermann,Th.Anker,M.Albiez,M.Taglieber,P.Treutlein,K.P.Marzlin,and M.K.Oberthaler.Bright Bose-Einstein Gap Solitons of Atoms with Repulsive Interaction[J].Phys.Rev.Lett.,2004,92:230401.
[152]A.Trombettoni and A.Smerzi.Discrete Solitons and Breathers with Dilute Bose-Einstein Condensates[J].Phys.Rev.Lett.,2001,86:2353-2356.
[153]T.Busch and J.R.Anglin.Motion of Dark Solitons in Trapped Bose-Einstein Condensates[J].Phys.Rev.Lett.,2000,84:2298-2301.
[154]A.D.Jackson,G.M.Kavoulakis,and C.J.Pethick.Solitary waves in clouds of Bose-Einstein condensed atoms[J].Phys.Rev.A,1998,58:2417-2422.
[155]G Huang,M.G.Velarde,and V.A.Makarov.Dark solitons and their head-on collisions in Bose-Einstein condensates[J].Phys.Rev.A,2001,64:013617.
[156]I.Carusotto,D.Embriaco,G.C.L.Rocca.Nonlinear atom optics and bright-gap-soliton generation in finite optical lattices[J].Phys.Rev.A,2002,65:053611.
[157]R.W.Boyd.Nonlinear Optics[M].London:Acadamics Press,1992.
[158]S.F.Mingaleev and Yuri S.Kivshar.Self-Trapping and Stable Localized Modes in Nonlinear Photonic Crystals[J].Phys.Rev.Lett.,2001,86:5474-5477.
[159]A.A.Sukhorukov,D.Neshev,W.Krolikowski,and Y.S.Kivshar.Nonlinear Bloch-Wave Interaction and Bragg Scattering in Optically Induced Lattices[J].Phys.Rev.Lett.2004,92:093901.
[160]A.V.Yulin,D.V.Skryabin.Out-of-gap Bose-Einstein solitons in optical lattices [J].Phys.Rev.A,2003,67:023611.
[161]E.A.Ostrovskaya,Y.S.Kivshar.Matter-Wave Gap Solitons in Atomic Band-Gap Structures[J].Phys.Rev.Lett.,2003,90:160407.
[162]Xiao-Fei Zhang,Qin Yang,Jie-Fang Zhang,X.Z.Chen,and W.M.Liu.Controlling soliton interactions in Bose-Einstein condensates by synchronizing the Feshbach resonance and harmonic trap[J].Phys.Rev.A,2008,77:023613.
[163]S.Burger,K.Bongs,S.Dotter,W.Etrier,and K.Penstock.Dark Solitons in Bose-Einstein Condensates[J].Phys.Rev.Lett.,1999,83:5198.
[164]B.P.Anderson,P.C.Halal,C.A.Regal,D.L.Feder,L.A.Collins,C.W.Clark,and E.A.Cornell.Watching Dark Solitons Decay into Vortex Rings in a Bose-Einstein Condensate[J].Phys.Rev.Lett.,2001,86:2926.
[165]J.Denschlag,J.E.Simsarian,D.L.Feder,Charles W.Clark,L.A.Collins,J.Cubizolles,L.Deng,Ei.W.Hagley,K.Helmerson,W.P.Reinhardt,S.L.Rolston,B.I.Schneider,and W.D.Phillips.Generating solitons by phase engineering of a Bose-Einstein condensate[J].Science,2000,287:97.
[166]Zachary Dutton,Michael Budde,Christopher Slowe,and Lene Vestergaard Hau.Generating Solitons by Phase Engineering of a Bose-Einstein Condensate[J].Science,2001,293:663.
[167]L.Khaykovich,F.Schreck,G.Ferrari,T.Bourdel,J.Cubizolles,L.D.Carr,Y.Castin,and C.Salomon.Formation of a Matter-Wave Bright Soliton[J].Science,2002,296:1290.
[168]K.E.Strecker,G.B.Partridge,A.G.Truscott,R.G.Hulet.Formation and propagation of matter-wave soliton trains[J].Nature,2002,417:150.
[169]B.Eiermann,Th.Anker,M.Albiez,M.Taglieber,P.Treutlein,K.-P.Marzlin,and M.K.Oberthaler.Bright Bose-Einstein Gap Solitons of Atoms with Repulsive Interaction[J].Phys.Rev.Lett.,2004,92:230401.
[170]A.J.Leggett.Bose-Einstein condensation in the alkali gases:Some fundamental concepts[J].Rev.Mod.Phys.,2001,73:307.
[171]J.Ieda,T.Miyakawa,and M.Wadati.Exact Analysis of Soliton Dynamics in Spinor Bose-Einstein Condensates[J].Phys.Rev.Lett.,93:194102.
[172]L.Li,Z.Li,B.A.Malomed,D.Mihalache,and W.M.Liu.Exact soliton solutions and nonlinear modulation instability in spinor Bose-Einstein condensates[J].Phys.Rev.A,2005,72:033611.
[173]L.Li,B.A.Malomed,D.Mihalache,and W.M.Liu.Exact soliton-on-plane-wave solutions for two-component Bose-Einstein condensates[J].Phys.Rev.E 2006,73:066610.
[174]W.Zhang,(O|¨)E.Miitecaplioglu,and L.You.Solitons in a trapped spin-1 atomic condensate[J].Phys.Rev.A,2007,75:043601.
[175]G.Thalhammer,G.Barontini,1 L.De Sarlo,J.Catani,F.Minardi,and M.Inguscio.Double Species Bose-Einstein Condensate with Tunable Interspecies Interactions [J].Phys.Rev.Lett.,2008,100:210402.
[176]S.B.Papp,J.M.Pino,and C.E.Wieman.Tunable Miscibility in a Dual-Species Bose-Einstein Condensate[J].Phys.Rev.Lett.,2008,101:040402.
[177]Sadhan K.Adhikari.Bright solitons in coupled defocusing NLS equation supported by coupling:Application to Bose-Einstein condensation[J].Physics Letters A,2005,346:179.
[178]F.Dalfovo,S.Giorgini,L.P.Pitaevskii,and S.Stringari.Theory of Bose-Einstein condensation in trapped gases[J].Rev.Mod.Phys.,1999,71:463.
[179]S.K.Adhikari.Coupled Bose-Einstein condensate:Collapse for attractive interaction [J].Phys.Rev.A,2001,63:043611.S.K.Adhikari.Stability and collapse of a hybrid Bose-Einstein condensate of atoms and molecules[J].Phys.Lett.A,2001,281:265.
[180]S.Inouye,M.R.Andrews,J.Stenger,H.J.Miesner,D.M.Stamper-Kurn,W.Ketterle.Observation of Feshbach resonances in a Bose + Einstein condensate[J].Nature,1998,392:151;Ph.Courteille,R.S.Freeland,D.J.Heinzen,F.A.van Abeelen,B.J.Verhaar.Observation of a Feshbach Resonance in Cold Atom Scattering [J].Phys.Rev.Lett.,1998,81:69.
[181]G.Thalhammer,G.Barontini,1 L.De Sarlo,J.Catani,F.Minardi,and M.Inguscio.Double Species Bose-Einstein Condensate with Tunable Interspecies Interactions [J].Phys.Rev.Lett.,2008,100:210402.
[182]S.B.Papp,J.M.Pino,and C.E.Wieman.Tunable Miscibility in a Dual-Species Bose-Einstein Condensate[J].Phys.Rev.Lett.,2008,101:040402.
[183]X.x.Liu,H Pu,B.Xiong,W.M.Liu,and J.b.Gong.Formation and transformation of vector solitons in two-species Bose-Einstein condensates with a tunable interaction[J].Phys.Rev.A,2009,79:013423.
[184]Tin-Lun Ho,V.B.Shenoy.Binary Mixtures of Bose Condensates of Alkali Atoms [J].Phys.Rev.Lett.,1996,77,3276.
[185]B.D.Esry,Chris H.Greene,James P.Burke,Jr.,and John L.Bohn.Hartree-Fock Theory for Double Condensates[J].Phys.Rev.Lett.,1997,78:3594.
[186]H.Pu and N.P.Bigelow.Collective Excitations,Metastability,and Nonlinear Response of a Trapped Two-Species Bose-Einstein Condensate[J].Phys.Rev.Lett.,1998,80:1134.
[2]S.N.Bose.Planck's law and light quantum hypothesis.Z.Phys.,1924,26:178-1711.
[3]A.Einstein.Quantentheorie des einatiomigen idealen Gases.Sitzungs-ber.Preuss.Akad.Wiss.,1924,1924:261.
[4]M.H.Anderson,J.R.Ensher,M.R.Matthews,C.E.Wieman,and E.A.Cornell.Observation of Bose-Einstein condensation in a dilute atomic vapor[j].Science,1995,269:198-201.
[5]K.B.Davis,M.O.Mewews,M.R.Andrews,N.J.van Druten,D.S.Durfee,D.M.Kurn,and W.Ketterle.Bose-Einstein condensation in a Gas of Sodium Atoms [J].Phys.Rev.Lett.,1995,75:3969-3973.
[6]C.C.Bradley,C.A.Sackett,J.J.Tollett,and R.G.Hulet.Evidence of Bose-Einstein Condensation in an Atomic Gas with Attractive Interactions[J].Phys.Rev.Lett.,1995,75:1687-1690.
[7]S.Burger,K.Bongs,S.Dettmer,W.Ertmer,K.Sengstock.Dark Solitons in Bose-Einstein Condensates[J].Phys.Rev.Lett.,1999,83:5198-5201.
[8]J.Denschlag,J.E.Simsarian,D.L.Feder,Charles W.Clark,L.A.Collins,J.Cubizolles,L.Deng,E.W.Hagley,K.Helmerson,W.P.Reinhardt,S.L.Rolston,B.I.Schneider,and W.D.Phillips.Generating Solitons by Phase Engineering of a Bose-Einstein Condensate[J].Science,2000,287:97-101.
[9]H.Saito and M.Ueda.Dynamically Stabilized Bright Solitons in a Two-Dimensional Bose-Einstein Condensate[J].Phys.Rev.Lett.,2003,90:040403.
[10]L.Khaykovich,F.Schreck,G.Ferrari,T.Bourdel,J.Cubizolles,L.D.Carr,Y.Castin,and C.Salomon.Formation of a Matter-Wave Bright Soliton[J].Science,2002,296:1290-1293.
[11]K.E.Strecker,G.B.Partridgel,A.G.Truscott,R.G.Hulet.Formation and propagation of matter-wave soliton trains[J].Nature,2002,417:150-153.
[12]Kaup D.J.A perturbation expansion for the Zakharov-Shabat inverse scattering transform[J].SIAM J.Appl.Math.,1976,31:121.
[13]Karpman V.I.Soliton evolution in the presence of perturbation[J].Phys.Scripta,1979,20:462.
[14]Maslov E.M.Second order perturbation theory for solitons[J].Teor.Mat.Fiz.,1980,42:362.
[15]Kivshar,Yu.S.and B.A.Malomed.Dynamics of solitons in nearly integrable systems [J].Rev.Mod.Phys.,1989,61:763.
[16]Gorshkov K.A.,and L.A.Ostrovsky.Interactions of solitons in nonintegrable systems:direct perturbation method and applications[J].Physica D,1981,428:1981.
[17]Ablowitz M.J,Clarkson P.A.Solitons,Nonlinear Evolution Equations and Inverse Scattering[M].London:Cambridge University Press,1991:149.
[18]Infled E,Rowlands G.Nonlinear Waves,Solitons and Chaos[M].England:Cambridge University Press,2000
[19]Rogers C,Schief W.K.B(a|¨)cklund and Darboux transformations geometry and mordern applications in soliton theory[M].UK:Cambridge University Press,Cambridge Texts in Applied Mathematics.2002.
[20]楼森岳,唐晓艳.非线性数学物理方法[M].北京:科学出版社,2006.
[21]Russell J.S.Report of the committee on waves.Rep.Meet,Brit.Assoc.Adv.Sci.7th Livepool,London,John Murray,1837:417.
[22]王明亮.非线性发展方程和孤立子[M].兰州:兰州大学出版社,1982.
[23]Zabusky N.J,Kruskal M.D.Interaction of “solitons” in a Collisionless Plasma and the Recurrence of Initial States[J].Phys.Rev.Lett.,1965,14:240.
[24]Haswgawa A,Tappert F.Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers[J].App.Phys.Lett,1973,23:142
[25]Gredeskul S.A,Kivshar Y.S.Generation of Dark Solitons in Optical Fiberslnteractions of solitons in nonintegrable systems:direct perturbation method[J].Phys.Rev.Lett,1989,62:977.
[26]Kumar A,Thomas Kurz,and Werner Lauterborn.Two-state bright solitons in doped fibers with saturating nonlinearity[J].Phys.Rev.E,1996,53:1166.
[27]A.Dreischuh,G.G.Paulus,F.Zacher,F.Grasbon,D.Neshev,and H.Walther.Modulational instability of multiple-charged optical vortex solitons under saturation of the nonlinearity[J].Phys.Rev.E,1999,60:7518.
[28]Carr L.D.Solitons in Bose-Einstein Condensates,doctor thesis,2001.
[29]Roberto Camassa and Darryl D.Holm.An integrable shallow water equation with peaked solitons[J].Phys.Rev.Lett.1993,71:1661-1664.
[30]S.Burger,K.Bongs,S.Dettmer,W.Ertmer,K.Sengstock,A.Sanpera,G.V.Shlyapnikov,and M.Lewenstein.Dark Solitons in Bose-Einstein Condensates[J].Phys.Rev.Lett,1999,83:5198.
[31]Jared C.Bronski,Lincoln D.Carr,Bernard Deconinck3,and J.Nathan Kutz.Bose-Einstein Condensates in Standing Waves:The Cubic Nonlinear Schrodinger Equation with a Periodic Potential[J].Phys.Rev.Lett,2001,86:1402-1405.
[32]Carr L.D,Clark C.W,and Reinhardt W.P.Stationary solutions of the one-dimensional nonlinear Schrodinger equation.I.Case of repulsive nonlinearity[J].Phys.Rev.A,2000,62:063610.
[33]C.S.Gardner,J.M.Greene,M.D.Kruskal and R.M.Miura.Method for solving the Korteweg-de Vries equation[J].Phys.Rev.Lett,1967,19:1095-1097.
[34]N.N.Huang.Theory of solitons and method of perturbation[M].Shanghai:Shanghai Scientific and Technological Education Publishing House,1996:1-99.
[35]R.Hirota.Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons[J].Phys.Rev.Lett,1971,27:1192-1194.
[36]刘式适和刘式达.物理学中的非线性方程[M].北京:北京大学出版社,2000:4-156.
[37]M.R.Miura.Backlund transformation[M].Berlin:Springer-Verlag,1978.
[38]C.Rogers and W.K.Shadwick.B(a|¨)cklund transformations and their applications [M].Academic Press,1982.
[39]M.L.Wang.Solitary wave solution for variant Boussineq equations[J].Phys.Lett.A.,1995,199:169-172.
[40]M.L.Wang.Exact solutions for a compound KdV-Burgers equation[J].Phys.Lett.A.,1996,213:279-287.
[41]M.L.Wang,Y.B.Zhou And Z.B.Li.Application of homogeneous balance method to exact solutions of nonlinear evolution equation in mathematical physics[J].Phys.Lett.A.,1996,216:67-75.
[42]E.G.Fan and H.Q.Zhang.New exact solutions to a system of coupled equations [J].Phys.Lett.A.,1998,245:389-392.
[43]D.J.Kaup.A perturbation expansion for the Zakharov-Shabat inverse scattering transform[J].SIAM J.Appl.Math.,1976,31:121-125.
[44]D.J.Kaup.Solitons as particles,oscillators,and in slowly changing media:a singular perturbation theory[J].Proc.R.Soc.A,1978,361:413-446.
[45]V.I.Karpman.Soliton evolution in the presence of perturbation[J].Phys.Scripta,1979,20:462-471.
[46]E.M.Maslov.Second order perturbation theory for solitons[J].Teor.Mat.Fiz.,1980,42:362-369.
[47]G.L.LAmb.Element of Soliton Theory[M].wiley:New York,1980:259-278
[48]Yu.S.Kivshar and B.A.Malomad.Dynamics of solitons in nearly integrable system[J].Rev.Mod.Phys.,1989,61:763-915.
[49]M.J.Ablowitz and P.A.Clarkson.Solitons,Nonlinear Evolution Equations and Inverse Scattering[M].England:Cambridge University Press,1991:31-38.
[50]V.M.Lashkin.Perturbation theory for dark solitons:Inverse scattering transform approach and radiative effects[J].Phys.Rev.E,2004,70:066620.
[51]K.A.Gorshkov and L.A.Ostrovskii.Interactions of solitons in non-integrable systems:direct perturbation method and applications[J].Physica D,1981,3(1):428-438.
[52]M.B.Fogel,S.E.Trullinger,A.R.Bishop and J.A.Krumhansl.Classical Particlelike Behavior of Sine-Gordon solitons in Scattering Potentials and Applied Fields[J].Phys.Rev.Lett.,1976,36:1411-1414.
[53]J.P.Keener and D.W.MClaughlin.Solitons under perturbations[J].Phys.Rev.A.,1977,16:777-790.
[54]R.L.Herman.A direct approach to studying soliton perturbation[J].J.Phys.A,1990,23:2327-2362
[55]V.V.Konotop and V.E.Vekslerchik.Direct perturbation theory for dark solitons [J].Phys.Rev.E,1994,49:2397-2407.
[56]X.J.Chen,Zh.D.Chen and N.N.Huang.Adirect perturbation theory for dark solitons based on a complete set of the squared Jost solutions[J].J.Phys.A,1998,31(2):6929-6947.
[57]J.R.Yan and Y.Tang.Direct approach to the study of soliton perturbation[J].Phys.Rev.E,1996,54:6816-6824.
[58]Y.Tang,J.R.Yah and Zh.H.Chen.Direct Approach for Kink Solution of φ-4Equation Under Perturbation[J].Chin.Phys.Lett,1997,14:845-848.
[59]J.R.Yah,Y.Tang and G.H.Zhou.Direct approach to the study of soliton perturbations of the nonlinear Schr(o|¨)dinger equation and the sine-Gordon equation[J].Phys.Rev.E,1998,58:1064-1073.
[60]F.Kh.Abdullaev,E.N.Tsoy,B.A.Malomed,and R.A.Kraenkel.Array of Bose-Einstein condensates under time-periodic Feshbach-resonance management [J].Phys.Rev.A,1998,68:053606.
[61]P.G.Kevrekidis,G.Theocharis,D.J.Frantzeskakis,and B.A.Malomed.Feshbach Resonance Management for Bose-Einstein Condensates[J].Phys.Rev.Lett.,2003,90:230401.
[62]G.Theocharis,P.Schmelcher,P.G.Kevrekidis,and D.J.Frantzeskakis.Matterwave solitons of collisionally inhomogeneous condensates[J].Phys.Rev.A,2005,72:033614
[63]Fatkhulla Kh.Abdullaev and Josselin Garnier.Propagation of matter-wave solitons in periodic and random nonlinear potentials[J].Phys.Rev.A,2005,72:061605(R)
[64]H.Sakaguchi and B.A.Malomed.Matter-wave solitons in nonlinear optical lattices [J].Phys.Rev.E,2005,72:046610.
[65]E.Ott and R.N.Sudan.Nonlinear theory of ion acoustic waves with Landau damping[J].Phys.Fluid.,1969,12:2388-2394
[66]K.Nozaki.Stochastic Instability of Sine-Gordon Solitons[J].Phys.Rev.Lett.,1982,49(26):1883-1885.
[67]B.A.Malomed and A.V.Ustinov.Pinning of a fluxion chain in a long Josephson Junction with a lattice of inhomogeneities:Theory and experiment[J].J.Appl.Phys.,1990,67:3791-3797
[68]D.J.Kaup.Thermal corrections to overdamped soliton motion[J].Phys.Rev.B,1983,27:6787-6795.
[69]D.J.Kaup.Perturbation theory for solitons in optical fibers[J].Phys.Rev.A,1990,42:5689-5694.
[70]D.J.Kaup.Second-order perturbations for solitons in optical fibers[J].Phys.Rev.A,1991,44(7):4582-4590
[71]M.B.Fogel,S.E.Trullinger,A.R.Bishop and J.A.Krumhansl.Dynamics of sine-Gordon solitons in the presence of perturbation[J].Phys.Rev.B,1977,15:1578-1592.
[72]J.R.Yan,Y.Tang and G.H.Zhou.First-order Correction of the perturbed Sine-Gordon Equation[J].Chin.Phys.Lett,1999,16:79-81
[73]J.R.Yan,Y.Tang and G.H.Zhou.Perturbation Theory for Nonlinear Klein-Gordon Kinks[J].Commun.Theor.Phys.,1999,32:375-382.
[74]J.R.Yan,L.X.Pan and G.H.Zhou.Soliton Perturbation for a Combined Kdv-MKdv Equation[J].Chin.Phys.Lett,2000,9:625-627.
[75]L.X.Pan,J.R.Yah and G.H.Zhou.Direct Approach for Soliton Perturbations Based on the Green's Function[J].Chin.Phys.,2001,7:594-598.
[76]Kaup,D.J.,J.Perturbation theory for solitons in optical fibers[J].Phys.Rev.A,1990,42:5689.
[77]Kaup D.J.Second-order perturbations for solitons in optical fibers.Phys.Rev.A,1991,44:4582.
[78]Herman R.J.A direct approach to studying soliton perturbations[J].J.Physics.A,1990,23:2327.
[79]Kivshar Y S and Malomed B A.Dynamics of solitons in nearly integrable systems.Rev.Mod.Phys.,1989,61:763.
[80]Li Zhi-Bin and Pan Su-Qi.广义五阶 KdV 方程的孤波解与孤子解[J].Acta Phys.Sin.,2001,50:402(in Chinese).
[81]Wei Cai-Min,Xia Zun-Quan and Tian Nai-Shuo.广义随机 KdV 方程新的精确类孤子解.Acta Phys.Sin.,2005,54:2463(in Chinese).
[82]S.N.Bose.Planck's law and light quantum hypothesis.Z.Phys.,1924,26:178-181.
[83]A.Einstein.Quantentheorie des einatomigen idealen Gases[J].Sitzungsber.Preuss.Akad.Wiss.,1924,1924:261.
[84]M.H.Anderson,J.R.Ensher,M.R.Matthews,C.E.Wieman,E.A.Cornell.Observation of Bose-Einstein condensation in a dilute atomic vapor[J].Science,1995,269:198-201.
[85]K.B.Davis,M.O.Mewes,M.R.Andrews,N.J.van Druten,D.S.Durfee,D.M.Kurn,and W.Ketterle.Bose-Einstein Condensation in a Gas of Sodium Atoms [J].Phys.Rev.Lett.,1995,75:3969-3973.
[86]C.C.Bradley,C.A.Sackett,J.J.Tollett,and R.G.Hulet.Evidence of Bose-Einstein Condensation in an Atomic Gas with Attractive Interactions.Phys.Rev.Lett.,1995,75:1687-1690.
[87]F.London.On the Bose-Einstein Condensation.Phys.Rev,1938,45:947-954.
[88]D.Hulin,A.Mysyrowicz,and C.Benoit Guillaume.Evidence for Bose-Einstein Statistics in an Exciton Gas.Phys.Rev.Lett.,1980,45:1970.
[89]J.L.Lin and J.P.Wolfe.Bose-Einstein condensation of paraexcitons in stressed Cu2O.Phys.Rev.Lett.,1993,71:1222.
[90]Jia Ling Lin and J.P.Wolfe.Bose-Einstein condensation of paraexcitons in stressed Cu_2O[J].Phys.Rev.Lett.,1993,71:1222-1225.
[91]C.J.Pethick and H.Smith.Bose-Einstein condensation in Dilute gases[M].Uk:Cambrige University Press,2002.
[92]D.J.Wineland,R.E.Drullinger,and F.L.Walls.Radiation-Pressure Cooling of Bound Resonant Absorbers[J].Phys.Rev.Lett.,1978,40:1639-1642.
[93]W.D.Phillips,H.Metcalf.Laser Deceleration of an Atomic Beam[J].Phys.Rev.Lett.,1982,48:596-599.
[94]D.G.Fried et al.Bose-Einstein Condensation of Atomic Hydrogen[J].Phys.Rev.Lett.,1998,81:3811-3814.
[95]S.Cornish,N.Claussen,J.Roberts,E.Cornell,C.Wieman.Stable 85Rb Bose-Einstein Condensates with Widely Tunable Interactions[J].Phys.Rev.Lett.,2000,85:1795-1798.
[96]G.Modugno,G.Ferrari,G.Roati,R.J.Brecha,A.Simoni,and M.Inguscio.Bose-Einstein Condensation of Potassium Atoms by Sympathetic Cooling[J].Science,2001,294:1320-1322.
[97]A.Robert,O.Sirjean,A.Browaeys,J.Poupard,S.Nowak,D.Boiron,C.I.Westbrook,and A.Aspect.A Bose-Einstein Condensate of Metastable Atoms[J].Science,2001,292:461-464.
[98]T.Weber et al.Bose-Einstein Condensation of Cesium[J].Science,2002,299:232-235.
[99]Yosuke Takasu,Kenichi Maki,Kaduki Komori,Tetsushi Takano,Kazuhito Honda,Mitsutaka Kumakura,Tsutomu Yabuzaki,and Yoshiro Takahashi.Spin-Singlet Bose-Einstein Condensation of Two-Electron Atoms[J].Phys.Rev.Lett.,2003,91:040404(4).
[100]T.Radu,H.Wilhelm,V.Yushankhai,D.Kovrizhin,R.Coldea,Z.Tylczynski,T.L(u|¨)hmann,and F.Steglich.Bose-Einstein Condensation of Magnons in Cs_2CuCl_4[J].Phys.Rev.Lett.,2005,95:127202(4).
[101]周蜀渝,龙全,周善钰,付海翔,王育竹.玻色-爱因斯坦凝聚在中国科学院上海光机所实现[J].物理,2002,31:481-482.
[102]F.Dalfovo,S.Giorgini,L.P.Pitaevskii,and S.Stringari.Theory of Bose-Einstein condensation in trapped gases[J].Rev.Mod.Phys.1999,71:463-512.
[103]A.J.Leggett.Bose-Einstein condensation in the alkali gases:Some fundamental concepts[J].Rev.Mod.Phys.,2001,73:307-356.
[104]C.J.Myatt,E.A.Burt,R.W.Ghrist,E.A.Cornell,C.E.Wieman.Production of Two Overlapping Bose-Einstein Condensates by Sympathetic Cooling[J].Phys.Rev.Lett.,1997,78,586.
[105]G.Modugno,M.Modugno,F.Riboli,G.Roati,M.Inguscio.Two Atomic Species Superfluid[J].Phys.Rev.Lett.,2002,89:190404.
[106]G.D.Telles,A.R.L.Caires,V.S.Bagnato,L.G.Marcassa.Observation of Ultracold Ground-State Heteronuclear Molecules[J].Phys.Rev.Lett.,2004,92:133203.
[107]S.B.Papp,C.E.Wieman.Observation of Heteronuclear Feshbach Molecules from a~(85)Rb-~(87)Rb Gas[J].Phys.Rev.Lett.,2006,97:180404.
[108]M.Modugno,F.Ferlaino,F.Riboli,G.Roati,G.Modugno.M.Inguscio.Meanfield analysis of the stability of a K-Rb Fermi-Bose mixture[J].Phys.Rev.A 2003,68:043626;C.Ospelkaus,S.Ospelkaus,L.Humbert,P.Ernst,K.Sengstock,K.Bongs.Ultracold Heteronuclear Molecules in a 3D Optical Lattice[J].Phys.Rev.Lett.,2006,97:120402
[109]D.M.Stamper-Kurn,M.R.Andrews,A.P.Chikkatur,S.Inouye,H.-J.Miesner,J.Stenger,and W.Ketterle,Optical Confinement of a Bose-Einstein Condensate,Phys.Rev.Lett.1998,80:2027-2030.
[110]M.D.Barrett,J.A.Sauer,and M.S.Chapman.All-Optical Formation of an Atomic Bose-Einstein Condensate[J].Phys.Rev.Lett.2001,87:010404(4).
[111]M.-S.Chang,C.D.Hamley,M.D.Barrett,J.A.Sauer,K.M.Fortier,W.Zhang,L.You,and M.S.Chapman.Observation of Spinor Dynamics in Optically Trapped ~(87)Rb Bose-Einstein Condensates[J].Phys.Rev.Lett.,2004,92:140403(4).
[112]P.Maddaloni,M.Modugno,C.Fort,F.Minardi,and M.Inguscio.Collective Oscillations of Two Colliding Bose-Einstein Condensates[J].Phys.Rev.Lett.,2000,85:2413-2417.
[113]C.J.Myatt,E.A.Burt,R.W.Ghrist,E.A.Cornell,and C.E.Wieman.Production of Two Overlapping Bose-Einstein Condensates by Sympathetic Cooling [J].Phys.Rev.Lett.,1997,78:586-589.
[114]D.S.Hall,M.R.Matthews,J.R.Ensher,C.E.Wieman,and E.A.Cornell.Dynamics of Component Separation in a Binary Mixture of Bose-Einstein Condensates [J].Phys.Rev.Lett.,1998,81:4531-4534.
[115]J.Williams,R.Walser,J.Cooper,E.Cornell,and M.Holland.Nonlinear Josephson-type oscillations of a driven,two-component Bose-Einstein condensate [J].Phys.Rev.A,1999,59:R31-R34.
[116]S.Inouye,M.R.Andrews,J.Stenger,H.J.Miesner,D.M.Stamper-Kurn,and W.Ketterle.Observation of Feshbach resonances in a Bose-Einstein condensate[J].Nature,1998,392:151-154.
[117]Markus Grelner,01af Mandel,Tllman Essllnger,Theodor W.Hansch,Immanuel Bloch.Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms[J].Natue,2002,415:39-44.
[118]Th.Busch and J.Anglin.Dark-Bright Solitons in Inhomogeneous Bose-Einstein Condensates[J].Phys.Rev.Lett,2001,87(1):010401.
[119]A.D.Jackson,G.M.Kavoulakis,and C.J.Pethick.Solitary waves in clouds of Bose-Einstein condensed atoms[J].Phys.Rev.A,1998,58(3):2417-2422.
[120]L.D.Carr,Charles W.Clark,and W.P.Reinhardt.Stationary solutions of the one-dimensional nonlinear Schrodinger equation.I.Case of repulsive nonlinearity[J].Phys.Rev.A,2000,62(6):063610.
[121]L.D.Carr,J.Brand,S.Burger et al.Dark-soliton creation in Bose-Einstein condensates[J].Phys.Rev.A,2001,63(5):051601.
[122]J.Dziarmaga and K.Sacha.Depletion of the dark soliton:The anomalous mode of the Bogoliubov theory[J].Phys.Rev.A,2002,66:043620.
[123]R.Dum,J.I.Cirac,M.Lewenstein,et al.Creation of Dark Solitons and Vortices in Bose-Einstein Condensates[J].Phys.Rev.Lett,1998,80(14):2972-2975.
[124]S.Burger,L.D.Carr,P.berg et al.Generation and interaction of solitons in Bose-Einstein condensates[J].Phys.Rev.A,2002,65:043611.
[125]D.J.Frantzeskakis,G.Theocharis,F.K.Diakonos,et al.Interaction of dark solitons with localized impurities in Bose-Einstein condensates[J].Phys.Rev.A,2002,66:053608.
[126]W.P.Zhang,D.F.Walls and B.C.Sanders.Atomic soliton in a traveling wave laser beam[J].Phys.Rev.Lett,1994,72(1):60-63.
[127]B.Wu,J.Liu and Q.Niu.Controlled Generation of Dark Solitons with Phase Imprinting[J].Phys.Rev.Lett,2002,88:034101.
[128]T.Hong,Y.Z.Wang,and Y.S.Huo.Temporal dark solitons in nonuniform Bose-Einstein condensates[J].Phys.Rev.A,1998,58(4):3128-3133.
[129]G.Huang,V.A.Makarov and M.G.Velarde.Two-dimensional solitons in Bose-Einstein condensates with a disk-shaped trap[J].Phys.Rev.A,2003,67:023604.
[130]G.Huang,Jacob Szefte and Shanhua Zhu.Dynamics of dark solitons in quasione-dimensional Bose-Einstein condensates[J].Phys.Rev.A,2002,65:053605.
[131]U.A.Khawaja,H.T.C.Stoof,R.G.Hulet,K.E.Strecker and G.B.Partridge.Bright Soliton Trains of Trapped Bose-Einstein Condensates[J].Phys.Rev.Lett.,2002,89:200404.
[132]V.Y.F.Leung,A.G.Truscott,K.G.H.Baldwin et al.Nonlinear atom optics with bright matter-wave soliton trains[J]Phys.Rev.A,2002,66:061602.
[133]L.D.Carr,Y.Castin Dynamics of a matter-wave bright soliton in an expulsive potential[J].Phys.Rev.A,2002,66:063602.
[134]U.Al.Khawajia,H.T.C.Stoof,R.G.Hulet,K.E.Strecker,and G.B.Partridge Bright Soliton Trains of Trapped Bose-Einstein condensates[J]Phys.Rev.Lett.,2002,89:200404.
[135]V.M.P(?)rez-Garc(?)a,H.Michinel,H.Herrero.Bose-Einstein solitons in highly asymmetric traps[J].Phys.Rev.A,1998,57:3837-3842.
[136]W.Hai,S.Huang and K.Gao.Wavepacket trains of a Paul trapped ion[J].J.Phys.B,2003,36:3055-3061.
[137]F.Kh.Abdullaev,and R.Galimzyanov.The dynamics of bright matter wave solitons in a quasi one-dimensional Bose-Einstein condensate with a rapidly varying trap[J].J.Phys.B,2003,36:1099-1108.
[138]H.Satio,and M.Ueda.Dynamically Stabilized Bright Solitons in a Two-Dimensional Bose-Einstein condensate[J].Phys.Rev.Lett.,2003,90:040403.
[139]M.R.Andrews,D.M.Kurn,H.J.Miesner,D.S.Durfee,C.G.Townsend,S.Inouye and W.Ketterle.Propagation of Sound in a Bose-Einstein condensate[J].Phys.Rev.Lett.,1997,79:553-556.
[140]F.Dalfovo and Stefano Giorgini.Theory of Bose-Einstein condensation in trapped gases[J].Rev.Mod.Phys.,1999,71(3):463-512.
[141]张礼,葛墨林.量子力学的前沿问题[M],北京:清华大学出版社,2000.
[142]S.Burger,K.Bongs,S.Dettmer,W.Ertmer,K.Sengstock,A.Sanpera,G.V.Shlyapnikov,and M.Lewenstein.Darl solitons in Bose-Einstein Condensates[J].Phys.Rev.Lett.,1999 83:5198.
[143]J.Denschlag,J.E.Simsarian,D.L.Feder,C.W.Clark,L.A.Collins,J.Cubizolles,L.Deng,E.W.Hagley,K.Helmerson,W.P.Reinhardt,S.L.Rolston,B.I.Schneider,W.D.Phillips.Generating Solitons by Phase Engineering of a Bose-Einstein Condensete[J].Science 2000,287:97.
[144]L.Dobrek,M.Gajda,M.Lewenstein,K.Sengstock,G.Birkl,W.Ertmer.Optical generation of vortices in trapped Bose-Einstein condensates[J].Phys.Rev.A,1999,60:R3381.
[145]S.Burger,L.D.Carr,P.Ohberg,K.Sengstock,A.Sanpera.Generation and interaction of solitons in Bose-Einstein condensates[J].Phys.Rev.A,2002,65:043611.
[146]H.Saito and M.Ueda.Dynamically Stabilized Bright Solitons in a Two-Dimensional Bose-Einstein Condensate[J].Phys.Rev.Lett.,2003,90:040403.
[147]L.Khaykovich,F.Schreck,G.Ferrari,T.Bourdel,J.Cubizolles,L.D.carr,Y.Castin,C.Salomon.Formation of a Matter-Wave Bright solion[J].Science 2002,296:1290-1293
[148]K.E.Strcker,G.B.Partridge,A.G.Truscott,R.G.Hulet.Formation and propagation of the matter-wave soliton trains[J].Nature,2002,417:150-153.
[149]Z.X.Liang,Z.D.Zhang,and W.M.Liu.Dynamics of a Bright Soliton in Bose-Einstein Condensates with Time-Dependent Atomic Scattering Length in an Expulsive Parabolic Potential[J].Phys.Rev.Lett.,2005,94:050402(4).
[150]P.J.Y.Louisl,E.A.Ostrovskaya,C.M.Savage,and Y.S.Kivshar.Bose-Einstein condensates in optical lattices:Band-gap structure and solitons[J].Phys.Rev.A,2003,67:013602.
[151]B.Eiermann,Th.Anker,M.Albiez,M.Taglieber,P.Treutlein,K.P.Marzlin,and M.K.Oberthaler.Bright Bose-Einstein Gap Solitons of Atoms with Repulsive Interaction[J].Phys.Rev.Lett.,2004,92:230401.
[152]A.Trombettoni and A.Smerzi.Discrete Solitons and Breathers with Dilute Bose-Einstein Condensates[J].Phys.Rev.Lett.,2001,86:2353-2356.
[153]T.Busch and J.R.Anglin.Motion of Dark Solitons in Trapped Bose-Einstein Condensates[J].Phys.Rev.Lett.,2000,84:2298-2301.
[154]A.D.Jackson,G.M.Kavoulakis,and C.J.Pethick.Solitary waves in clouds of Bose-Einstein condensed atoms[J].Phys.Rev.A,1998,58:2417-2422.
[155]G Huang,M.G.Velarde,and V.A.Makarov.Dark solitons and their head-on collisions in Bose-Einstein condensates[J].Phys.Rev.A,2001,64:013617.
[156]I.Carusotto,D.Embriaco,G.C.L.Rocca.Nonlinear atom optics and bright-gap-soliton generation in finite optical lattices[J].Phys.Rev.A,2002,65:053611.
[157]R.W.Boyd.Nonlinear Optics[M].London:Acadamics Press,1992.
[158]S.F.Mingaleev and Yuri S.Kivshar.Self-Trapping and Stable Localized Modes in Nonlinear Photonic Crystals[J].Phys.Rev.Lett.,2001,86:5474-5477.
[159]A.A.Sukhorukov,D.Neshev,W.Krolikowski,and Y.S.Kivshar.Nonlinear Bloch-Wave Interaction and Bragg Scattering in Optically Induced Lattices[J].Phys.Rev.Lett.2004,92:093901.
[160]A.V.Yulin,D.V.Skryabin.Out-of-gap Bose-Einstein solitons in optical lattices [J].Phys.Rev.A,2003,67:023611.
[161]E.A.Ostrovskaya,Y.S.Kivshar.Matter-Wave Gap Solitons in Atomic Band-Gap Structures[J].Phys.Rev.Lett.,2003,90:160407.
[162]Xiao-Fei Zhang,Qin Yang,Jie-Fang Zhang,X.Z.Chen,and W.M.Liu.Controlling soliton interactions in Bose-Einstein condensates by synchronizing the Feshbach resonance and harmonic trap[J].Phys.Rev.A,2008,77:023613.
[163]S.Burger,K.Bongs,S.Dotter,W.Etrier,and K.Penstock.Dark Solitons in Bose-Einstein Condensates[J].Phys.Rev.Lett.,1999,83:5198.
[164]B.P.Anderson,P.C.Halal,C.A.Regal,D.L.Feder,L.A.Collins,C.W.Clark,and E.A.Cornell.Watching Dark Solitons Decay into Vortex Rings in a Bose-Einstein Condensate[J].Phys.Rev.Lett.,2001,86:2926.
[165]J.Denschlag,J.E.Simsarian,D.L.Feder,Charles W.Clark,L.A.Collins,J.Cubizolles,L.Deng,Ei.W.Hagley,K.Helmerson,W.P.Reinhardt,S.L.Rolston,B.I.Schneider,and W.D.Phillips.Generating solitons by phase engineering of a Bose-Einstein condensate[J].Science,2000,287:97.
[166]Zachary Dutton,Michael Budde,Christopher Slowe,and Lene Vestergaard Hau.Generating Solitons by Phase Engineering of a Bose-Einstein Condensate[J].Science,2001,293:663.
[167]L.Khaykovich,F.Schreck,G.Ferrari,T.Bourdel,J.Cubizolles,L.D.Carr,Y.Castin,and C.Salomon.Formation of a Matter-Wave Bright Soliton[J].Science,2002,296:1290.
[168]K.E.Strecker,G.B.Partridge,A.G.Truscott,R.G.Hulet.Formation and propagation of matter-wave soliton trains[J].Nature,2002,417:150.
[169]B.Eiermann,Th.Anker,M.Albiez,M.Taglieber,P.Treutlein,K.-P.Marzlin,and M.K.Oberthaler.Bright Bose-Einstein Gap Solitons of Atoms with Repulsive Interaction[J].Phys.Rev.Lett.,2004,92:230401.
[170]A.J.Leggett.Bose-Einstein condensation in the alkali gases:Some fundamental concepts[J].Rev.Mod.Phys.,2001,73:307.
[171]J.Ieda,T.Miyakawa,and M.Wadati.Exact Analysis of Soliton Dynamics in Spinor Bose-Einstein Condensates[J].Phys.Rev.Lett.,93:194102.
[172]L.Li,Z.Li,B.A.Malomed,D.Mihalache,and W.M.Liu.Exact soliton solutions and nonlinear modulation instability in spinor Bose-Einstein condensates[J].Phys.Rev.A,2005,72:033611.
[173]L.Li,B.A.Malomed,D.Mihalache,and W.M.Liu.Exact soliton-on-plane-wave solutions for two-component Bose-Einstein condensates[J].Phys.Rev.E 2006,73:066610.
[174]W.Zhang,(O|¨)E.Miitecaplioglu,and L.You.Solitons in a trapped spin-1 atomic condensate[J].Phys.Rev.A,2007,75:043601.
[175]G.Thalhammer,G.Barontini,1 L.De Sarlo,J.Catani,F.Minardi,and M.Inguscio.Double Species Bose-Einstein Condensate with Tunable Interspecies Interactions [J].Phys.Rev.Lett.,2008,100:210402.
[176]S.B.Papp,J.M.Pino,and C.E.Wieman.Tunable Miscibility in a Dual-Species Bose-Einstein Condensate[J].Phys.Rev.Lett.,2008,101:040402.
[177]Sadhan K.Adhikari.Bright solitons in coupled defocusing NLS equation supported by coupling:Application to Bose-Einstein condensation[J].Physics Letters A,2005,346:179.
[178]F.Dalfovo,S.Giorgini,L.P.Pitaevskii,and S.Stringari.Theory of Bose-Einstein condensation in trapped gases[J].Rev.Mod.Phys.,1999,71:463.
[179]S.K.Adhikari.Coupled Bose-Einstein condensate:Collapse for attractive interaction [J].Phys.Rev.A,2001,63:043611.S.K.Adhikari.Stability and collapse of a hybrid Bose-Einstein condensate of atoms and molecules[J].Phys.Lett.A,2001,281:265.
[180]S.Inouye,M.R.Andrews,J.Stenger,H.J.Miesner,D.M.Stamper-Kurn,W.Ketterle.Observation of Feshbach resonances in a Bose + Einstein condensate[J].Nature,1998,392:151;Ph.Courteille,R.S.Freeland,D.J.Heinzen,F.A.van Abeelen,B.J.Verhaar.Observation of a Feshbach Resonance in Cold Atom Scattering [J].Phys.Rev.Lett.,1998,81:69.
[181]G.Thalhammer,G.Barontini,1 L.De Sarlo,J.Catani,F.Minardi,and M.Inguscio.Double Species Bose-Einstein Condensate with Tunable Interspecies Interactions [J].Phys.Rev.Lett.,2008,100:210402.
[182]S.B.Papp,J.M.Pino,and C.E.Wieman.Tunable Miscibility in a Dual-Species Bose-Einstein Condensate[J].Phys.Rev.Lett.,2008,101:040402.
[183]X.x.Liu,H Pu,B.Xiong,W.M.Liu,and J.b.Gong.Formation and transformation of vector solitons in two-species Bose-Einstein condensates with a tunable interaction[J].Phys.Rev.A,2009,79:013423.
[184]Tin-Lun Ho,V.B.Shenoy.Binary Mixtures of Bose Condensates of Alkali Atoms [J].Phys.Rev.Lett.,1996,77,3276.
[185]B.D.Esry,Chris H.Greene,James P.Burke,Jr.,and John L.Bohn.Hartree-Fock Theory for Double Condensates[J].Phys.Rev.Lett.,1997,78:3594.
[186]H.Pu and N.P.Bigelow.Collective Excitations,Metastability,and Nonlinear Response of a Trapped Two-Species Bose-Einstein Condensate[J].Phys.Rev.Lett.,1998,80:1134.