关于KdV方程孤子解的研究  

The Research on the Soliton Solution to the KdV Equation

作　　者：何进春[1] 黄念宁[2] 

机构地区：[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

出　　处：《应用数学》2007年第1期145-150,共6页Mathematica Applicata

基　　金：华中科技大学博士后专项基金资助课题(0101011110)

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.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.

关 键 词：KDV方程 反散射法 GEL fand—Levitan—Marchenko方程 

分 类 号：O175.29[理学—数学] O411.1[理学—基础数学]