The new tri-function method to multiple exact solutions of nonlinear wave equations. (English) Zbl 1155.35427

Summary: Based on a system of the first order differential equations with three nonlinear ordinary differential equations (ODEs), a new tri-function method is presented to investigate exact solutions of a wide class of nonlinear wave equations. The method is constructive and can be carried out in a computer with the aid of symbolic computation. In particular, we apply the tri-function method to the \((3+1)\)-dimensional Kadomtsev-Petviashvili (KP) equation and the \((2+1)\)-dimensional nonlinear Schrödinger (NLS) equation such that many types of new exact solutions are obtained, which contain doubly periodic solutions and solitary wave solutions.


35Q51 Soliton equations
35Q53 KdV equations (Korteweg-de Vries equations)
35Q58 Other completely integrable PDE (MSC2000)
35B10 Periodic solutions to PDEs
35A25 Other special methods applied to PDEs
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