摘要
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 Painlevd 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.
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 Painlevd 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.
基金
Supported by the National Natural Science Foundations of China under Grant Nos 10735030, 10475055, 10675065 and 90503006, the National Basic Research Program of China under Grant No 2007CB814800, PCSIRT （IRT0734）, the Research Fund of Post- doctoral of China under Grant No 20070410727, and the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No 20070248120.
