关键词: nonlinear wave, perturbation, computer algebra, renormalization technique, approximate analytical method of characteristics, anisotropy, viscoelasticity, wave equation, eigen theory

Abstract: 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-term uniformly valid solution is obtained with the symbolic computation by using a computer algebra system. The comparison of the derived asymptotic solution dnd the numerical solution shows that they coincide with each other for smaller ε and agree quite well for larger ε(e. g., e=0.25)

Key words: nonlinear wave, perturbation, computer algebra, renormalization technique, approximate analytical method of characteristics, anisotropy, viscoelasticity, wave equation, eigen theory