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含自相容源的可积系统 被引量：1

Integrable System with Self-consistent Sources
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摘要 含自相容源的可积方程(SESCSs)是一类重要的非线性偏微分方程,研究其可积性和寻求其精确解都具有重要的数学意义,SESCSs描述的是不同孤波间的相互作用,又有重要的物理意义。这类方程也正丰富了Lax可积系统的内容。从可积意义上详细介绍了含自相容源的可积方程,与求解此类方程有关的构造含自相容源的可积方程的方法。给出Lax可积的概念,作为例子,给出了含自相容源的非等谱KdV方程族、含自相容源的非等谱AKNS方程族及其Lax表示。 The integrable equations with self-consistent sources is one kind of important nonlinear evolution equations. The studies of its integrable and solutions have important mathematics senses. It is used to describe interactions between different solitary waves and has important physical applications. We introduce the concept of Lax integrable and give the hierarchy of the non-isospectral KdV equation with self-consistent sources （ KdVESCS ） and the hierarchy of the non-isospectral AKNS equation with self-consistent sources（ AKNS ESCS ） as examples.
作者 李琪
机构地区 东华理工大学数学与信息科学学院
出处 《东华理工大学学报（自然科学版）》 CAS 2009年第1期93-96,共4页 Journal of East China University of Technology(Natural Science)
基金 东华理工大学校长基金项目(DHXK0810)
关键词 含自相容源的可积方程 Lax可积 integrable equations with self-consistent sources Lax Representation
分类号 O175.24 [理学—基础数学]
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参考文献7

  • 1Hu X,Wang H.2006.Construction of dKP and BKP equations with self-consistent sources Inverse Problems 22:1903-20.
  • 2Leon J,Latifi A.1990.Solutions of an initial-boundary value problem for coupled nonlinear waves[J].Phys A 23:1385-403.
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  • 7Zhang D.2002.The N-soliton solutions of the MKdV equation with self-consistent sources[J].Phys Soc Jpn 71:2649-56.

同被引文献12

  • 1Ablowitz M J, Clarkson P A. 1991. Solitons, Nonlinear Evolution E-quation and Inverse Scattering[ M] . Cambridge : Cambridge University Press.
  • 2Ablowitz M J, Prinari B, Trubatch A D. 2004. Discrete and Continuous Nonlinear Schrodinger Systems [ M]. Cambridge : Cambridge University Press.
  • 3Akhmediev N, Ankiewicz A. 2011. Modulation instability, Fermi-Pas-ta-Ulam recurrence, rogue waves, nonlinear phase shift, and exact solutions of the Ablowitz-Ladik equation [ J]. Physical Review E,83 (4): 046603-10.
  • 4Ankiewicz A, Akhmediev N, Soto-Crespo J M. 2010. Discrete roguewaves of the Ablowitz-Ladik and Hirota equations[ J]. Physical Review E, 82(8) : 026602-7.
  • 5Geng X G,Dai H H,Zhang J Y. 2007. Decomposition of the discrete Ablowitz-Ladik hierarchy [ J ]. Studies in Applied Mathematics, 118 (3) : 281-312.
  • 6Guo B L, Ling L M. 2011. Rogue Wave, Breathers and Bright-Dark-Rogue Solutions for the Coupled Schrodinger Equations[ J]. Chinese Physics Letters, 28(11) : 110202-4.
  • 7Hirota R. 1971. Exact solution of the KdV equation for multiple collisions of solitons[ J]. Physical Review Letters, 27( 18) : 1192- 4.
  • 8Zhang D J,Chen S T. 2010. Symmetries for the Ablowitz - Ladik Hierarchy :Part I. Four-Potential Case [ J ]. Studies in Applied Mathematics, 125(4) : 393-418.
  • 9Zhang D J, Chen S T. 2010. Symmetries for the Ablowitz - Ladik Hierarchy :Part II. Integrable Discrete Nonlinear Schrodinger Equations and Discrete AKNS Hierarchy[ J]. Studies in Applied Mathematics, 125(4) : 419-443.
  • 10高云,乐励华.Zakharov-Kuznetsov方程新的周期解和孤立波解[J].东华理工大学学报（自然科学版）,2010,33(4):393-397. 被引量：5

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东华理工大学学报（自然科学版）
2009年 第1期

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