Abstract It is difficult to obtain exact solutions of the nonlinear partial differential equations (PDEs) due to the 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 system. A simple invariant expansion with quite a universal pseudopotential is used for some nonlinear PDEs such as Korteweg-de Vries (KdV) equation with fifth-order dispersion term, perturbed fourth-order KdV equation, KdV-Burgers equation, and Boussinesq type of equation.
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11175092), Scientific Research Fund of Zhejiang Provincial Education Department (Grant No. Y201017148), and K. C. Wong Magna Fund in Ningbo University.
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