The new tri-function method to multiple exact solutions of nonlinear wave equations

Abstract

In this paper, 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.