一个非线性波动方程的计算机代数－摄动解

Computer Algebra-Perturbation Solution to a Nonlinear Wave Equation

本文采用计算机代数－摄动法讨论一个非线性波动方程的Ｃａｙｃｈｙ问题高阶渐近解，将特征坐标变形与重整化方法相结合，消除直接展开解的长期项，并利用计算机代数软件进行符号运算，得到该问题的四项摄动解，所得的渐近解与数值解的比较表明：对较小的ε，两者相吻合；对较大的ε（如ε＝０．２５），两者也相当符合。

In this paper,the higher-order asymptotic solution to the Cauchy problem of a nonlinear wave equation is found by using a computer algebra-perturbation method.The secular terms in the solution from straightforward expansions are eliminated with the straining of characteristic coordinates and the use of the renormalization technique, and the four-teru uniformly valid solution is obtained with the symbolic computation using a computer algebra system. The comparison of the derived asymptotic solution and the numerical solution shows that they coincide with each other for smaller ε and agree quite well for larger ε (e.g.,ε=0.25).