非线性波方程准确孤立波解的符号计算

数学物理学报 ›› 1997, Vol. 17 ›› Issue (1): 81-89.

非线性波方程准确孤立波解的符号计算

李志斌, 张善卿

兰州大学数学系兰州 730000

收稿日期:1995-03-14 修回日期:1996-03-22 出版日期:1997-02-26 发布日期:1997-02-26
基金资助:
国家自然科学基金;甘肃省自然科学基金资助

Exact Solitary Wave Solutions for Nonlinear Wave Equations Using Symbolic Computation

Li Zhibin, Zhang Shanqing

Department of Mathematics. Lanzhou University, Lanzhou. 730000. PR China

Received:1995-03-14 Revised:1996-03-22 Online:1997-02-26 Published:1997-02-26

摘要/Abstract

摘要： 该文将机械化数学方法应用于偏微分方程领域,建立了构造一类非线性发展方程孤立波解的一种统一算法,并在计算机数学系统上加以实现,推导出了一批非线性发展方程的精确孤立波解.算法的基本原理是利用非线性发展方程孤立波解的局部性特点,将孤立波表示为双曲正切函数的多项式.从而将非线性发展方程(组)的求解问题转化为非线性代数方程组的求解问题.利用吴文俊消元法在计算机代数系统上求解非线性代数方程组,最终获得非线性发展方程(组)的准确孤立波解.

关键词: 非线性波方程, 孤立波解, 符号计算

Abstract: In this paper the Mathematics-Mechanization method is applied the field of differential equations. A unifying algorithm for constructing solitary wave solutions for a class of nonlinear evolution equations are given, and implemented in a.computer algebraic system.Exact solitary wave solutions of a great deal of nonlinear equations are obtained. The algorithm is based on the fact that the solitary wave solutions are essentially of a localized nature. Seeking solitary wave solutions which are in terms of hyperbolic tangent function gives a nonlinear system of algebraic equations. The system is solved by using Wu Elimination and the exact solutions of nonlinear evolution equation(s) are then obtained.

Key words: Nonlinear evolution equations, Solitary wave solutions, Symbolic computation

李志斌, 张善卿. 非线性波方程准确孤立波解的符号计算[J]. 数学物理学报, 1997, 17(1): 81-89.

Li Zhibin, Zhang Shanqing. Exact Solitary Wave Solutions for Nonlinear Wave Equations Using Symbolic Computation[J]. Acta mathematica scientia,Series A, 1997, 17(1): 81-89.

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[2]	张辉群. 耦合Klein-Gordon-Schrdinger方程的孤立波解[J]. 数学物理学报, 2002, 22(3): 332-335.