广义耦合KdV孤子方程的达布变换及其偶孤子解

数学物理学报 ›› 2009, Vol. 29 ›› Issue (5): 1213-1222.

广义耦合KdV孤子方程的达布变换及其偶孤子解

西南大学数学与统计学院应用数学系四川重庆 400715

收稿日期:2007-11-08 修回日期:2008-10-09 出版日期:2009-10-25 发布日期:2009-10-25
基金资助:
西南大学学校青年基金(SWUQ2006028)资助

Darboux Transformation of Generalized Coupled KdV Soliton Equation and its Even-soliton Solutions

Department of Applied Mathematics, School of Mathematics and Statistics, Southwest University, Sichuan Chongqing 400715

Received:2007-11-08 Revised:2008-10-09 Online:2009-10-25 Published:2009-10-25
Supported by:
西南大学学校青年基金(SWUQ2006028)资助

摘要/Abstract

摘要：

根据广义耦合KdV孤子方程的Lax对, 借助谱问题的规范变换, 一个包含多参数的达布变换被构造出来. 利用达布变换来产生广义耦合KdV孤子方程的偶孤子解, 并且用行列式的形式来表达广义耦合KdV孤子方程的偶孤子解. 作为应用, 广义耦合KdV孤子方程的偶孤子解的前两个例子被给出.

关键词: 达布变换, 孤子方程, 偶孤子解, 规范变换

Abstract:

Based on the resulting Lax pairs of the generalized coupled KdV soliton equation, a new Darboux transformation with multi-parameters for the generalized coupled KdV soliton equation is derived with the help of a gauge transformation of the spectral problem. By using the Darboux transformation, the generalized even-soliton solutions of the generalized coupled KdV soliton equation are given and presented in determinant form. As an application, the first two cases are given.

Key words: Darboux transformation, Soliton equation, Even-soliton solution, Gauge transformation

中图分类号:

35Q51

刘萍. 广义耦合KdV孤子方程的达布变换及其偶孤子解[J]. 数学物理学报, 2009, 29(5): 1213-1222.

LIU Ping. Darboux Transformation of Generalized Coupled KdV Soliton Equation and its Even-soliton Solutions[J]. Acta mathematica scientia,Series A, 2009, 29(5): 1213-1222.

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