群速度与相速度对层级结构NSLE一孤子解的影响
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摘要
基于具有层级结构的非线性薛定谔方程(NLSE),得到了该方程的一孤子解及其相速度和群速度,并详细讨论了相速度与群速度的关系对一孤子传输特性的影响。结果表明:当相速度和群速度不相等时,一孤子解的实部和虚部具有不同的特性和周期;当相速度和群速度相等时,一孤子解的实部和虚部的周期性消失。
Based on the hierarchy of nonlinear Schrdinger equation(NLSE),the one-soliton solution of the equation and its phase velocity and group velocity are obtained.Influence of the relationship between the phase velocity and group velocity on the one-soliton's transmission is discussed detailedly.And the results show that,the real and imaginary parts of the one-soliton solution have different characteristics and periods when the phase velocity and group velocity are not equal.When the phase velocity and group velocity are equal,the periodicity of the real and imaginary parts disappear.
Based on the hierarchy of nonlinear Schrdinger equation(NLSE),the one-soliton solution of the equation and its phase velocity and group velocity are obtained.Influence of the relationship between the phase velocity and group velocity on the one-soliton's transmission is discussed detailedly.And the results show that,the real and imaginary parts of the one-soliton solution have different characteristics and periods when the phase velocity and group velocity are not equal.When the phase velocity and group velocity are equal,the periodicity of the real and imaginary parts disappear.
引文
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[19]Hirota R.Exact Envelope Soliton Solutions of a Nonlinear Wave Equation[J].J math phys,1973,14(7):805-809.DOI:10.1063/1.1666399.
[20]Ankiewicz A,Soto-Crespo J M,Akhmediev N.Rogue Waves and Rational Solutions of the Hirota Equation[J].Physical Review E Statistical Nonlinear&Soft Matter Physics,2010,81(4Pt 2):046602.DOI:https:∥doi.org/10.1103/PhysRevE.81.046602.
[21]Chowdury A,Kedziora D J,Ankiewicz A,et al.Soliton Solutions of an Integrable Nonlinear Schr9dinger Equation with Quintic Terms[J].Phys Rev E Stat Nonlin Soft Matter Phys,2014,90(3):032922.DOI:https:∥doi.org/10.1103/PhysRevE.90.032922.
[22]Hoseini S M,Marchant T R.Solitary Wave Interaction and Evolution for a Higher-order Hirota Equation[J].Wave Motion,2006,44(2):92-106.DOI:https:∥doi.org/10.1016/j.wavemoti.2006.08.001.
[2]Akhmediev N N,Ankiewicz A.Solitons:Nonlinear Pulses and Beams[M].Chapman&Hall,1997.
[3]Hasegawa A,Tappert F.Transmission of Stationary Nonlinear Optical Pulses in Dispersive Dielectric Fibers.I.Anomalous Dispersion[J].Applied Physics Letters,1973,23(3):142-144.DOI:10.1063/1.1654836.
[4]Agrawal G P.Nonlinear Fiber Optics(Fourth Edition)[M].2006.DOI:10.1007/3-540-46629 09.
[5]Zakharov V E.Stability of Periodic Waves of Finite Amplitude on the Surface of a Deep Fluid[J].Journal of Applied Mechanics and Technical Physics,1972,9(2):190-194.DOI:10.1007/BF00913182.
[6]Kharif C,Pelinovsky E,Slunyaev A.Rogue Waves in the Ocean[M].Springer Berlin Heidelberg,2009.DOI:10.1007/978-3-540-88419-4.
[7]ANDREEV P A.FIRST Principles Derivation of Nls Equation for Bec with Cublc and Quintic Nonlinearities at Nonzero Temperature:Dispersion of Linear Waves[J].International Journal of Modern Physics B,2013,27(6):1350017.DOI:10.1142/S0217979213500173.
[8]Peregrine D H.Water Waves,Nonlinear Schr9dinger Equations and Their Solutions[J].J Australian Math Soc Ser B,1983,25(1):16-43.DOI:https:∥10.1017/S0334270000003891.
[9]Vishnu P N,Senthilvelan M,Lakshmanan M.Akhmediev Breathers,Ma solitons,and General Breathers from Rogue Waves:A Case Study in the Manakov System[J].Physical Review E Statistical Nonlinear&Soft Matter Physics,2013,88(2):022918.DOI:10.1103/PhysRevE.88.022918.
[10]Frisquet B,Kibler B,Millot G.Collision of Akhmediev Breathers in Nonlinear Fiber Optics[J].Physical Review X,2013,3(3):041032.DOI:10.1103/PhysRevX.3.041032.
[11]Kedziora D J,Ankiewicz A,Akhmediev N.Second-order Nonlinear Schrodinger Equation Breather Solutions in the Degenerate and Rogue Wave Limits[J].Physical Review E Statistical Nonlinear&Soft Matter Physics,2012,85(2):066601.DOI:10.1103/PhysRevE.85.066601.
[12]Berge L,Skupin S,Lederer F,et al.Spatial BreakP.A.up of Femtosecond Laser Pulses in the Atmosphere[J].Physica Scripta,2004,2004(5):135.DOI:10.1238/Physica.Topical.107a00135.
[13]Agrawal G P.Nonlinear Fiber Optics,Third[J].Lecture Notes in Physics,2001,18(1):195P.A.211.DOI:10.1007/3-540-46629-0-9.
[14]Hasegawa A,Tappert F.Hasegawa,A.&Tappert,F.Transmission of Stationary Nonlinear Optical Pulses in Dispersive Dielectric Fibers.Appl.Phys.Lett.23,142-144[J].Applied Physics Letters,1973,23(3):142-144.DOI:10.1063/1.1654836.
[15]Remoissenet M.Low-amplitude Breather and Envelope Solitons in Quasi-one-dimensional Physical Models[J].Physical Review B,1986,33(4):2386-2392.DOI:10.1103/PhysRevB.33.2386.
[16]Ankiewicz A,Akhmediev N.Rogue Wave Solutions for the Infinite Integrable Nonlinear Schr9dinger Equation Hierarchy[J].Physical Review E,2017,96(1-1):012219.DOI:https:∥doi.org/10.1103/PhysRevE.96.012219.
[17]Kano T.Normal Form of Nonlinear Schr9dinger Equation[J].Journal of the Physical Society of Japan,1989,58(12):4322-4328.DOI:10.1143/JPSJ.58.4322.
[18]Chowdury A,Krolikowski W.Breather-to-soliton Transformation Rules in the Hierarchy of Nonlinear Schr9dinger Equations[J].Phys rev e,2017,95(6):062226.DOI:10.1103/PhysRevE.95.062226.
[19]Hirota R.Exact Envelope Soliton Solutions of a Nonlinear Wave Equation[J].J math phys,1973,14(7):805-809.DOI:10.1063/1.1666399.
[20]Ankiewicz A,Soto-Crespo J M,Akhmediev N.Rogue Waves and Rational Solutions of the Hirota Equation[J].Physical Review E Statistical Nonlinear&Soft Matter Physics,2010,81(4Pt 2):046602.DOI:https:∥doi.org/10.1103/PhysRevE.81.046602.
[21]Chowdury A,Kedziora D J,Ankiewicz A,et al.Soliton Solutions of an Integrable Nonlinear Schr9dinger Equation with Quintic Terms[J].Phys Rev E Stat Nonlin Soft Matter Phys,2014,90(3):032922.DOI:https:∥doi.org/10.1103/PhysRevE.90.032922.
[22]Hoseini S M,Marchant T R.Solitary Wave Interaction and Evolution for a Higher-order Hirota Equation[J].Wave Motion,2006,44(2):92-106.DOI:https:∥doi.org/10.1016/j.wavemoti.2006.08.001.