Approximate Homotopy Direct Reduction Method: Infinite Series Reductions to Perturbed mKdV Equations

¹Department of Physics, Shanghai Jiao Tong University, Shanghai 200030 ²Department of Physics, Ningbo University, Ningbo 315211 ³School of Computer Science, Shaanxi Normal University, Xi'an 710062 ⁴School of Mathematics, Fudan University, Shanghai 200433

Received Date: January 28, 2009

Published Date: March 31, 2009

Abstract

An approximate homotopy direct 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 solutions 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 also valid for strong perturbations.