| 广义耦合KdV孤子方程的达布变换及其奇孤子解 |
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| 引用本文： | 刘萍.广义耦合KdV孤子方程的达布变换及其奇孤子解[J].应用数学和力学,2008,29(3):361-368. |
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| 作者姓名： | 刘萍 |
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| 作者单位： | 西南大学,数学与统计学院,应用数学系,重庆,400715 |
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| 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.
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| 关 键 词： | 达布变换 孤子方程 奇孤子解 规范变换 耦合 孤子方程 达布变换 孤子解 Solutions Soliton Equation Coupled Generalized Transformation 应用 表达 行列式 利用 规范变换 谱问题 |
| 文章编号： | 1000-0887（2008）03-0361-08 |
| 收稿时间： | 2007-09-28 |
| 修稿时间： | 2008-01-16 |
Darboux Transformation of Generalized Coupled KdV Soliton Equation and Its Odd-Soliton Solutions |
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| LIU Ping.Darboux Transformation of Generalized Coupled KdV Soliton Equation and Its Odd-Soliton Solutions[J].Applied Mathematics and Mechanics,2008,29(3):361-368. |
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| Authors: | LIU Ping |
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| 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. |
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| Keywords: | Darboux transformation soliton equation odd-soliton solution gauge transformation |
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