带有阻尼项的非线性波动方程的精确解

Exact solutions for a class of nonlinear wave equations with damping term

研究了出现在非线性振动中的一类带阻尼项的非线性波动方程.首先讨论了所论方程的行波解及其极限行为,其次借助于分离变量方法获得了所研究方程的一些显式精确解,讨论了这些解的极限行为.这些解有助于定性或数值分析非线性波动方程解的性态.

This paper deals with a class of nonlinear wave equations with damping term arising in nonlinear vi-bration. Traveling wave solutions and their limit behavior of the equation are first discussed. With the aid of method of separation of variables, some explicit and exact solutions of the equation are obtained then. The limit behavior of these solutions are also analyzed. These solutions are helpful for analysing the behavior of solutions of nonlinear wave equations analytically and numerically.