## 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.

### MSC:

 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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