New Periodic Solitary-Wave Solutions to the (3+1)-  Dimensional Kadomtsev-Petviashvili Equation

Zitian Li,Zhengde Dai,Jun Liu

doi:10.3390/mca15050877

Abstract

By the extended homoclinic test technique, explicit solutions of the (3+1)-dimensional Kadomtsev-Petviashvili(KP) equation are obtained. These solutions include doubly periodic wave solutions, doubly soliton solutions and periodic solitary-wave solutions. It is shown that the extended homoclinic test technique is a straightforward and powerful mathematical tool for solving nonlinear evolution equation.

Highlights

Many effective and powerful methods have been proposed to solve nonlinear evolution equations, such as the inverse scattering transform [1], the tanh function method [2], the homogeneous balance method [3], the auxiliary function method [4], the Exp-function method [5,6,7,8] and so on.Very recently, a new technique called "extended homoclinic test technique"was proposed [9] and has been applied to seek periodic solitary wave solutions of integrable equations [10,11]
By introducing different ansätz test function F(x, y, z, t) to Eq (3), we can obtain a series of exact solutions to the (3+1)D KP equation (1). (1) Suppose that the test function F(x, y, z, t) has the following ansätz: F(x, y, z, t)
(4) we suppose that the test function F(x, y, z, t) has the following ansätz: F

Summary

Introduction

Many effective and powerful methods have been proposed to solve nonlinear evolution equations, such as the inverse scattering transform [1], the tanh function method [2], the homogeneous balance method [3], the auxiliary function method [4], the Exp-function method [5,6,7,8] and so on.Very recently, a new technique called "extended homoclinic test technique"was proposed [9] and has been applied to seek periodic solitary wave solutions of integrable equations [10,11]. A new technique called "extended homoclinic test technique"was proposed [9] and has been applied to seek periodic solitary wave solutions of integrable equations [10,11]. We apply the technique to the (3+1)-dimensional KP equation. 2. PROCEDURES FOR SOLVING THE (3+1)D KP EQUATION

Results

Conclusion