非线性演化方程的孤立波解(英文)  

Solitary Wave Solutions for Nonlinear Evolution Equations

作　　者：王明亮[1] 李向正[1] 聂惠[1] 

机构地区：[1]河南科技大学理学院

出　　处：《应用数学》2006年第3期460-468,共9页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of Education Depart ment of HenanProvince of China (2006110002) ,the Science Foundation of Henan University of Science and Technology(2004ZD002 ,2006ZY001)

摘　　要：用齐次平衡原则和辅助微分方程方法得到了6个重要的n次非线性演化方程的孤立波解.辅助微分方程方法的主要思想是借助简单的可解微分方程的解去构造复杂的非线性演化方程的行进波解.这里简单的可解微分方程称为辅助微分方程.本文使用的辅助方程有双曲正割幂型解或双曲正切幂型解.The solitary wave solutions for six important nonlinear evolution equations with n degree nonlinearity are obtained by the homogeneous balance principle and sub-ODE method （mean by subsidiary ordinary differential equation method）. The main idea of the sub-ODE method is that the travelling wave solutions of a complicated nonlinear evolution equation can be constructed by means of the solutions of a simple and solvable ODE that is called sub-ODE. The sub-ODEs used in this paper admit the solutions of sech-power or tanh-power type.

关 键 词：n次非线性 广义KDV方程 广义BOUSSINESQ方程 广义BURGERS方程 辅助微分方程方法 

分 类 号：O175.2[理学—数学]