Exact Solitary Wave Solutions for Nonlinear Wave Equations Using Symbolic Computation
Exact Solitary Wave Solutions for Nonlinear Wave Equations Using Symbolic Computation
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发表时间：
1997
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通讯作者：
P. China
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作者：
P. China
本文将数学机械化方法应用于微分方程领域。给出了构造一类非线性发展方程孤立波解的统一算法，并在a.computer代数系统中实现，得到了大量非线性方程的精确孤立波解.该算法是基于这样一个事实，孤立波解本质上是一个本地化的性质。求出以双曲正切函数表示的孤立波解，得到一个非线性代数方程组。利用吴消元法求解该方程组，得到了非线性发展方程的精确解。
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.