近似摄动同伦约化方法：两个摄动mKdV方程的无穷级数约化
Approximate perturbed direct homotopy reduction method: infinite series reductions to two perturbed mKdV equations
摘要：
提出了一种近似摄动直接同伦约化方法，并将其应用于两个具有四阶色散和二阶耗散的摄动修正Korteweg-de Vries（mKdV）方程.推导出了任意阶的相似约化方程。该方法不仅适用于单孤子解，而且适用于Painlevé II波和Jacobi椭圆函数表示的四阶色散和二阶耗散的周期波。该方法对强扰动也是有效的。
英文摘要：
An approximate perturbed direct homotopy reduction method is proposed and applied to two perturbed modified Korteweg-de Vries (mKdV) equations with fourth order dispersion and second order dissipation. The similarity reduction equations are derived to arbitrary orders. The method is valid not only for single soliton solution but also for the Painlevé II waves and periodic waves expressed by Jacobi elliptic functions for both fourth order dispersion and second order dissipation. The method is valid also for strong perturbations.
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