广义耦合KdV孤子方程的达布变换及其奇孤子解

Darboux Transformation of Generalized Coupled KdV Soliton Equation and Its Odd-Soliton Solutions

Department of Applied Mathematics, School of Mathematics and Statistics, Southwest University, Chongqing 400715, P. R. China

摘要: 借助谱问题的规范变换, 给出广义耦合KdV孤子方程的达布变换,利用达布变换来产生广义耦合KdV孤子方程的奇孤子解,并且用行列式的形式来表达广义耦合KdV孤子方程的奇孤子解．作为应用,广义耦合KdV孤子方程奇孤子解的前两个例子被给出．
- 达布变换 /
- 孤子方程 /
- 奇孤子解 /
- 规范变换
Abstract: Based on the resulting Lax pairs of generalized coupled KdV soliton equation, a new Darboux transformation with multi-parameters for generalized coupled KdV soliton equation is derived with the help of a gauge transformation of the spectral problem. By using Darboux transformation, the generalized odd-soliton solutions of ceneralized coupled KdV soliton equation are given and presented in determinant form. As an application, the first two cases are given.
- Darboux transformation /
- soliton equation /
- odd-soliton solution /
- gauge transformation

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