Approximate solutions of nonlinear PDEs by the invariant expansion

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.