摘要
首先用行波变换将非线性偏微分方程转化为非线性常微分方程,然后采用摄动方法直接求解该非线性常微分方程,最后求得了非线性K le in-Gordon方程的二级近似解。这种方法也可进一步推广用于求其它非线性偏微分方程的近似解析解。
In this paper, nonlinear partial differential equation is transformed to nonlinear ordinary differential equation by virtue of traveling wave transformation method, and then straightforwardly solve it by taking advantage of perturbation method. Fi- nally, the second order approximate solutions of nonlinear Klein-Cordon equation are successfully obtained. It is not difficult to see that this method used herein is particularly simple and concise. We firmly believe that this approach used in our paper may be generalized to construct the approximately analytical sohtions to other nonlinear partial differential equations.
出处
《湖南人文科技学院学报》
2005年第5期15-17,44,共4页
Journal of Hunan University of Humanities,Science and Technology
关键词
非线性KLEIN-GORDON方程
行波变换
摄动解法
二级近似解
nonlinear Klein-Cordon equation
traveling wave transformation
perturbation method
second order approximate solution
