学术
摘 要:
mKdV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解满足两个相容性方程的方法,解决了这个问题.[著者文摘]
文章出处:
《应用数学》-2007年20卷4期 -808-813页
文献标识码:
A
文章编号:
1001-9847（2007）04-0808-06
Verification of the N-soliton Solution to the mKdV Equation
HE Jin-chun , HUANG Nian-ning （ Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, China ; Department of Physics, Wuhan University, Wuhan 430072, China）
Abstract:
It is difficult to verify the N- soliton solution of the mKdV 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 satis- fies the two compatibility equations. Secondly,we verify the N- soliton solution of the mKdV equation if we prove that these conditions can be demonstrate by the GLM e.cluation whic.h determine the Kernal function K（x,y,t） in according to the inverse scattering method. ＇[著者文摘]
Key words:
mKdV equation; The inverse scattering method; ZS-AKNS form; Gel＇fand-Levitan-Marchenko equation
基金资助:
华中科技大学博士后专项基金资助项目（0101011110）
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