Approximate direct reduction method:infinite series reductions to the perturbed mKdV equation  

作　　者：焦小玉 楼森岳 

机构地区：[1]Department of Physics,Shanghai Jiao Tong University [2]Department of Physics,Ningbo University

出　　处：《Chinese Physics B》2009年第9期3611-3615,共5页中国物理B（英文版）

基　　金：supported by the National Natural Science Foundations of China (Grant Nos 10735030,10475055,10675065 and 90503006);National Basic Research Program of China (Grant No 2007CB814800);PCSIRT (Grant No IRT0734);the Research Fund of Postdoctoral of China (Grant No 20070410727);Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No 20070248120)

摘　　要：The approximate direct reduction method is applied to the perturbed mKdV equation with weak fourth order dispersion and weak dissipation. The similarity reduction solutions of different orders conform to formal coherence, accounting for infinite series reduction solutions to the original equation and general formulas of similarity reduction equations. Painleve Ⅱ type equations, hyperbolic secant and Jacobi elliptic function solutions are obtained for zeroorder similarity reduction equations. Higher order similarity reduction equations are linear variable coefficient ordinary differential equations.The approximate direct reduction method is applied to the perturbed mKdV equation with weak fourth order dispersion and weak dissipation. The similarity reduction solutions of different orders conform to formal coherence, accounting for infinite series reduction solutions to the original equation and general formulas of similarity reduction equations. Painleve Ⅱ type equations, hyperbolic secant and Jacobi elliptic function solutions are obtained for zeroorder similarity reduction equations. Higher order similarity reduction equations are linear variable coefficient ordinary differential equations.

关 键 词：perturbed mKdV equation approximate direct reduction method series reduction solutions 

分 类 号：O175.29[理学—数学]