| 关于KdV方程孤子解的研究 |
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| 引用本文： | 何进春,黄念宁.关于KdV方程孤子解的研究[J].应用数学,2007,20(1):145-150. |
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| 作者姓名： | 何进春 黄念宁 |
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| 作者单位： | 1. 华中科技大学数学系,湖北,武汉,430074
2. 武汉大学物理学院,湖北,武汉,430072 |
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| 基金项目： | 华中科技大学校科研和教改项目 |
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| 摘 要： | KdV方程的多孤子解很难直接验证，本文通过证明GLM反散射变换方程导出的Jost解满足两个Lax方程的方法，解决了这个问题．
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| 关 键 词： | KdV方程 反散射法 Gel'fand-Levitan-Marchenko方程 |
| 文章编号： | 1001-9847(2007)01-0145-06 |
| 修稿时间： | 2006-06-12 |
The Research on the Soliton Solution to the KdV Equation |
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| HE Jin-chun,HUANG Nian-ning.The Research on the Soliton Solution to the KdV Equation[J].Mathematica Applicata,2007,20(1):145-150. |
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| Authors: | HE Jin-chun HUANG Nian-ning |
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| Institution: | 1. Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074 ,China ; 2. Department of Physics, Wuhan University, Wuhan 430072 ,China |
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| Abstract: | It is difficult to verify the N-soliton solution of the KdV equation derectly.In the paper,We find a method to solve the problem.The method is as follows:Firstly,Using the integral representation of the Jost solution,we deduce some conditions involving the kernal function K(x,y,t)if the Jost solution satisfies the two Lax equations.Secondly,we verify the N-soliton solution of the KdV equation if we prove that these conditions can be demonstrate by the GLM equation which determine the kernal function K(x,y,t)in according to the inverse scattering method. |
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| Keywords: | KdV equation The inverse scattering method Gel'fand-Levitan-Marchenko equation |
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