Modified Simple Equation Method and its Applications to Nonlinear Partial Differential Equations

Abstract: In this paper, the modified simple equation method is used to construct exact periodic and soliton solutions of some nonlinear partial differential equations. Exact solutions of the nonlinear Schrödinger equation, the Hamiltonian amplitude equation, Klein-Gordon equation in 1+2 dimension, the coupled Klein-Gordon equation, the (2 + 1)-dimensional long-wave-short-wave resonance interaction equation, the modified KdV-KP equation and the modified Benjamin-Bona-Mahony equation are successfully obtained. These solutions may be important of significance for the explanation of some practical physical problems.

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