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非线性波方程准确孤立波解的符号计算
引用本文: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(A辑),1997,17(1):81-89.
作者姓名:李志斌  张善卿
作者单位:兰州大学数学系!兰州,730000,兰州大学数学系!兰州,730000
基金项目:国家自然科学基金,甘肃省自然科学基金
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

Exact Solitary Wave Solutions for Nonlinear Wave Equations Using Symbolic Computation
Li Zhibin ,Zhang Shanqing.Exact Solitary Wave Solutions for Nonlinear Wave Equations Using Symbolic Computation[J].Acta Mathematica Scientia,1997,17(1):81-89.
Authors:Li Zhibin  Zhang Shanqing
Institution:Department of Mathematics. Lanzhou University. Lanzhou. 730000. PR China
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.
Keywords:Nonlinear evolution equations  Solitary wave solutions  Symbolic computation
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