摘要
非线性发展方程描述的系统中大量存在孤立波这种重要的非线性现象，求非线性发展方程的精确解是人们关心的问题，现已存在有较通用的反散射方法，以及对特定方程的非线性函数变换方法．近十年来人们利用计算机代数，考虑番列维分析或是待定系数方法，对大部分已知的非线性发展方程求得了方程的精确特解．本文以广义Ｋｕｒａｍｏｔｏ－Ｓｉｖａｓｈｉｎｓｋｙ（ｇＫＳ）方程为例，应用齐次平衡方法以及吴文俊消元法得到ｇＫＳ方程的孤立波解．说明结合这两种方法求非线性发展方程的精确特解，是一种快速而有效的方法．
The solitary wave is an important nonlinear phenomenon can be shown in nonlinear evolution equations. So, the IST (inverse scattering transform) method and the nonlinear transformation method have been applied in solving nonlinear evolution equations. Now based on Painleve property or property of hyperbolic functions, the exact solution of the mainly nonlinear evolution equations has been gotten with the computer algebra. Pro. Wu Wenjun considered the elimination method of the nonlinear algebraic equation (Wu elimination method) and created the mathematics automated method, which has been successfully applied in automated theorem proving, system science, computer science, etc. The exact solution of some evolution equations has been found by use of a homogeneous balance method introduced by Pro. Wang Mingliang. Using the homogeneous balance method, we can get a nonlinear transformation for evolution equations, and using the nonlinear transformation, we can get the exact solution easily. In this paper, the exact solutions of a generalized Kuramoto-Sivashinsky equations are obtained by using homogeneous balance method and Wu elimination method. The results show that It is an economical way to obtain solitary wave solutions of nonlinear evolution equations by using the two method.
出处
《兰州大学学报（自然科学版）》
CAS
CSCD
北大核心
1998年第4期53-55,共3页
Journal of Lanzhou University(Natural Sciences)
基金
国家自然科学基金
关键词
gKS方程
孤立波解
齐次平衡法
吴文俊消元法
gKS equation solitary wave solution homogeneous balance method Wu elimination method
