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

Yan, Zhenya

Phys. Scr. 78, No. 3, Article ID 035001, 5 p. (2008).

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

Keywords:

tri-function method; nonlinear wave equations; Kadomtsev-Petviashvili equation; nonlinear Schrödinger equation