Approximate solutions of nonlinear PDEs by the invariant expansion  

作　　者：吴江龙 楼森岳 

机构地区：[1]Faculty of Science,Ningbo University [2]Center of Nonlinear Science,Ningbo University

出　　处：《Chinese Physics B》2012年第12期31-36,共6页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Grant No.11175092);Scientific Research Fund of Zhejiang Provincial Education Department(Grant No.Y201017148);K.C.Wong Magna Fund in Ningbo University

摘　　要：It is difficult to obtain exact solutions of the nonlinear partial differential equations （PDEs） due to their complexity and nonlinearity, especially for non-integrable systems. In this paper, some reasonable approximations of real physics are considered, and the invariant expansion is proposed to solve real nonlinear systems. A simple invariant expansion with quite a universal pseudopotential is used for some nonlinear PDEs such as the Korteweg-de Vries （KdV） equation with a fifth-order dispersion term, the perturbed fourth-order KdV equation, the KdV-Burgers equation, and a Boussinesq-type equation.It is difficult to obtain exact solutions of the nonlinear partial differential equations （PDEs） due to their complexity and nonlinearity, especially for non-integrable systems. In this paper, some reasonable approximations of real physics are considered, and the invariant expansion is proposed to solve real nonlinear systems. A simple invariant expansion with quite a universal pseudopotential is used for some nonlinear PDEs such as the Korteweg-de Vries （KdV） equation with a fifth-order dispersion term, the perturbed fourth-order KdV equation, the KdV-Burgers equation, and a Boussinesq-type equation.

关 键 词：approximate solution invariant expansion Mobious transformation invariance 

分 类 号：O175.29[理学—数学] O353.2[理学—基础数学]