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.
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
