Spatiotemporal deformation of multi-soliton to (2聽+聽1)-dimensional KdV equation

详细信息    查看全文

• 作者：Jun Liu ; Gui Mu ; Zhengde Dai ; Hongying Luo
• 关键词：( $$2+1$$ 2 + 1 )D KdV equation ; Hirota method ; Three ; wave method ; Multi ; soliton ; Spatiotemporal deformation
• 刊名：Nonlinear Dynamics
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：83
• 期：1-2
• 页码：355-360
• 全文大小：608 KB
• 参考文献：1.Zabusky, N.J., Kruskal, M.D.: Interaction of solitons in a collisionaless plasma and the recurrence of initial states. Phys. Rev. Lett. 15, 240鈥?43 (1965)CrossRef
  2.Ablowitz, M.J., Clarkson, P.A.: Solitons, nonlinear evolution equations and inverse scattering, vol. 149. Cambridge University Press, Cambridge (1999)
  3.Weiss, J., Tabor, M., Carnevale, G.: The Painlev茅 property for partial differential equation. J. Math. Phys. 24, 522 (1983)CrossRef MathSciNet
  4.Pogrebkov, A.K.: On the formulation of the Painlev茅 test as a criterion of complete integrability of partial differential equation. Inverse Probl. 5(1), L7鈥揕10 (1989)CrossRef MathSciNet
  5.Weiss, J.: The Painlev茅 property for partial differential equations, II: B盲cklund transformation, Lax pairs, and the Schwarzian derivative. J. Math. Phys. 24, 1405 (1983)CrossRef MathSciNet
  6.Steeb, W.H., Kloke, M., Spieker, B.M.: Liouville equation, Painlev茅 property and B盲cklund transformation. Z. Naturforsch. A 38, 1054鈥?055 (1983)MathSciNet
  7.Weiss, J.: The sine-Gordon equations: complete and partial integrability. J. Math. Phys. 25, 2226 (1984)CrossRef MathSciNet
  8.Musette, M., Conte, R.: Algorithmic method for deriving Lax pairs from the invariant Painlev茅 analysis of nonlinear partial differential equations. J. Math. Phys. 32, 1450鈥?457 (1991)CrossRef MathSciNet
  9.Lou, S.Y.: Searching for higher dimensional integrable models from lower ones via Painlev茅 analysis. Phys. Rev. Lett. 80, 5027 (1998)CrossRef MathSciNet
  10.Ma, W.X., Huang, T.W., Zhang, Y.: A multiple exp-function method for nonlinear differential equations and its application. Phys. Scr. 82, 065003 (2010)CrossRef
  11.Ma, W.X., Fan, E.G.: Linear superposition principle applying to Hirota bilinear equations. Comput. Math. Appl. 61, 950鈥?59 (2011)CrossRef MathSciNet
  12.Ma, W.X.: Complexiton solutions to the Korteweg鈥揹e Vries equation. Phys. Lett. A 301, 35鈥?4 (2002)CrossRef MathSciNet
  13.Ma, W.X., You, Y.: Solving the Korteweg鈥揹e Vries equation by its bilinear form: Wronskian solutions. Trans. Am. Math. Soc. 357, 1753鈥?778 (2005)CrossRef MathSciNet
  14.Qin, Z.Y.: On periodic wave solution and asymptotic property of KdV鈥揝awada鈥揔otera equation. J. Phys. Soc. Jpn. B 76, 124004 (2007)CrossRef
  15.Tang, X.Y., Lou, S.Y., Zhang, Y.: Localized excitations in (2 + 1)-dimensional systems. Phys. Rev. E 66, 046601 (2002)CrossRef MathSciNet
  16.Meng, J.P., Zhang, J.F.: Nonpropagating solitary waves in (2 + 1)-dimensional nonlinear systems. Commun. Theor. Phys. 43, 831鈥?36 (2005)CrossRef MathSciNet
  17.Zheng, C.L., Fang, J.P., Chen, L.Q.: New variable separation excitations of (2 + 1)-dimensional dispersive long-water wave system obtained by an extended mapping approach. Chaos Solitons Fractals 23, 1741鈥?748 (2005)MathSciNet
  18.Fu, H.M., Dai, Z.D.: Double exp-function method and application. Int. J. Nonlinear Sci. Numer. Simul. 10(7), 927鈥?34 (2009)CrossRef
  19.Lou, S.Y.: Symmetries and algebras of the integrable dispersive long wave equations in (2 + 1)-dimensional spaces. J. Phys. A Math. 27, 3235 (1994)CrossRef
  20.Wang, J.W., Li, H.X., Wu, H.N.: Distributed proportional plus second-order spatial derivative control for distributed parameter systems subject to spatiotemporal uncertainties. Nonlinear Dyn. 76(4), 2041鈥?058 (2014)CrossRef MathSciNet
  21.Jiang, Y., Tian, B., Liu, W.J.: Solitons, B盲cklund transformation and Lax pair for the (2 + 1)-dimensional Boiti鈥揕eon鈥揚empinelli equation for the water waves. J. Math. Phys. 51(9), 093519鈥?93519-11 (2010)CrossRef MathSciNet
  22.Liu, W.J., Lei, M.: Types of coefficient constraints of coupled nonlinear Schr枚dinger equations for elastic and inelastic interactions between spatial solitons with symbolic computation. Nonlinear Dyn. 76(4), 1935鈥?941 (2014)CrossRef MathSciNet
  23.Peng, Y.Z., Krishnan, E.V.: The singular manifold method and exact periodic wave solutions to a restricted BLP dispersive long wave system. Rep. Math. Phys. 56(3), 367鈥?78 (2005)CrossRef MathSciNet
  24.Rosenau, P.: Nonlinear dispersion and compact structures. Phys. Rev. Lett. 73, 1737鈥?741 (1994)CrossRef MathSciNet
  25.Garagash, T.I.: Modification of the Painlev茅 test for systems of nonlinear partial differential equations. Theor. Math. Phys. 100, 1075 (1994)CrossRef MathSciNet
  26.Boiti, M., Leon, J.P., Manna, M., Pempinelli, F.: On the spectral transform of a Korteweg鈥揹e Vries equation in two spatial dimensions. Inverse Probl. 2, 271鈥?79 (1986)CrossRef MathSciNet
  27.Dorizzi, B., Grammaticos, B., Ramani, A., Winternitz, P.: Are all the equations of the Kadomtsev鈥揚etviashvili hierarchy integrable? J. Math. Phys. 27, 2848 (1986)CrossRef MathSciNet
  28.Tamizhmani, K.M., Punithavathi, P.: The infinite-dimensional lie algebraic structure and the symmetry reduction of a nonlinear higher-dimensional equation. J. Phys. Soc. Jpn. 59, 843鈥?47 (1990)CrossRef MathSciNet
  29.Peng, Y.Z.: New B盲cklund transformation and new exact solutions to (2 + 1)-dimensional KdV equation. Commun. Theor. Phys. (Beijing, China) 40, 257鈥?58 (2003)CrossRef
  30.Zhang, H., Ma, W.X.: Extended transformed rational function method and applications to complexiton solutions. Appl. Math. Comput. 230, 509鈥?15 (2014)CrossRef
  31.Xu, Z., Chen, H., Jiang, M., Dai, Z., Chen, W.: Resonance and deflection of multi-soliton to the (2 + 1)-dimensional Kadomtsev鈥揚etviashvili equation. Nonlinear Dyn. 78(1), 461鈥?66 (2014)CrossRef MathSciNet
  32.Mirzazadeh, M., Eslami, M., Biswas, A.: 1-Soliton solution of KdV6 equation. Nonlinear Dyn. 80, 387鈥?96 (2015)CrossRef MathSciNet
  33.Razborova, P., Triki, H., Biswas, A.: Perturbation of dispersive shallow water waves. Ocean Eng. 63, 1鈥? (2013)CrossRef
  34.Razborova, P., Kara, A.H., Biswas, A.: Additional conservation laws for Rosenau鈥揔dV鈥揜LW equation with power law nonlinearity by Lie symmetry. Nonlinear Dyn. 79(1), 743鈥?48 (2015)CrossRef MathSciNet
  35.Biswas, A.: Solitary wave solution for KdV equation with power law nonlinearity and time-dependent coefficients. Nonlinear Dyn. 58, 345鈥?48 (2009)CrossRef
  36.Bhrawy, A.H., Abdelkawy, M.A., Biswas, A.: Cnoidal and snoidal wave solutions to coupled nonlinear wave equations by the extended Jacobi鈥檚 elliptic function method. Commun. Nonlinear Sci. Numer. Simul. 18, 915鈥?25 (2013)CrossRef MathSciNet
  37.Bhrawy, A.H., Biswas, A., Javidi, M., Ma, W.X., Pinar, Z., Yildirim, A.: New solutions for (1 + 1)-dimensional Kaup鈥揔uperschmidt equations. Results Math. 63, 675鈥?86 (2013)CrossRef MathSciNet
  38.Bhrawy, A.H., Abdelkawy, M.A., Kumar, S., Johnson, S., Biswas, A.: Solitons and other solutions to quantum Zakharov鈥揔uznetsov equation in quantum magneto-plasmas. Indian J. Phys. 87, 455鈥?63 (2013)CrossRef
  39.Bhrawy, A.H., Abdelkawy, M.A., Kumar, S., Biswas, A.: Solitons and other solutions to Kadomtsev鈥揚etviashvili equation of B-type. Rom. J. Phys. 58, 729鈥?48 (2013)MathSciNet
  40.Ebadi, G., Fard, N.Y., Bhrawy, A.H., Kumar, S., Triki, H., Yildirim, A., Biswas, A.: Solitons and other solutions to the (3 + 1)-dimensional extended Kadomtsev鈥揚etviashvili equation with power law nonlinearity. Rom. Rep. Phys. 65, 27鈥?2 (2013)
  41.Biswas, A., Bhrawy, A.H., Abdelkawy, M.A., Alshaery, A.A., Hilal, E.M.: Symbolic computation of some nonlinear fractional differential equations. Rom. J. Phys. 59, 433鈥?42 (2014)
  42.Triki, H., Kara, A.H., Bhrawy, A., Biswas, A.: Soliton solution and conservation law of Gear鈥揋rimshaw model for shallow water waves. Acta Phys. Pol. A 125, 1099鈥?106 (2014)CrossRef
  43.Triki, H., Mirzazadeh, M., Bhrawy, A.H., Razborova, P., Biswas, A.: Soliton and other solutions to long-wave short wave interaction equation. Rom. J. Phys. 60, 72鈥?6 (2015)
  44.Bhrawy, A.H., Abdelkawy, M.A., Biswas, A.: Topological solitons and cnoidal waves to a few nonlinear wave equations in theoretical physics. Indian J. Phys. 87, 1125鈥?131 (2013)CrossRef
  
• 作者单位：Jun Liu (1)
  Gui Mu (1)
  Zhengde Dai (2)
  Hongying Luo (1)
  
  1. College of Mathematics and Information Science, Qujing Normal University, Qujing, 655011, People鈥檚 Republic of China
  2. School of Mathematics and Statistics, Yunnan University, Kunming, 650091, People鈥檚 Republic of China
  
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems and Control
  Mechanics
  Mechanical Engineering
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-269X

文摘

This work proposes a three-wave method with a perturbation parameter to obtain exact multi-soliton solutions of nonlinear evolution equation. The (\(2+1\))-dimensional KdV equation is used as an example to illustrate the effectiveness of the suggested method. Using this method, new multi-soliton solutions are given. Specially, spatiotemporal dynamics of breather two-soliton and multi-soliton including deformation between bright and dark multi-soliton each other, and deflection with different directions and angles are investigated and exhibited to (\(2+1\))D KdV equation. Some new nonlinear phenomena are revealed under the small perturbation of parameter. Keywords (\(2+1\) )D KdV equation Hirota method Three-wave method Multi-soliton Spatiotemporal deformation