Asymptotic solving method for period solution to a class of disturbed nonlinear evolution equation

A class of disturbed evolution equation is considered using a simple and valid technique. We first introduce periodic traveling-wave solution of a corresponding typical evolution equation. And then the approximate solution for an original disturbed evolution equation is obtained using the asymptotic method. And we point out that the series of approximate solution is convergent and the accuracy of the asymptotic solution is studied using the fixed point theorem for the functional analysis.