Classification of All Single Traveling Wave Solutions to (3 + 1)-Dimensional Breaking Soliton Equation

Yang Li

doi:10.4236/jamp.2014.24006

Abstract

In order to get the exact traveling wave solutions to nonlinear partial differential equation, the complete discrimination system for polynomial and direct integral method are applied to the considered equation. All single traveling wave solutions to the equation can be obtained. As an example, we give the solutions to (3 + 1)-dimensional breaking soliton equation.

Highlights

For the past decades, to deal with nonlinear partial differential equations (PDEs), many methods have been developed
To deal with nonlinear partial differential equations (PDEs), many methods have been developed. These methods have been widely applied to many PDEs to obtain the exact solutions
A method named the complete discrimination system for polynomial method has been proposed by Liu [1]-[5]

Summary

Introduction

To deal with nonlinear partial differential equations (PDEs), many methods have been developed. These methods have been widely applied to many PDEs to obtain the exact solutions. By Liu’s method, we can obtain the classification of single traveling wave solutions to some PDEs. For the PDE being considered, we take the traveling wave transformation and integrate it. By Liu’s method, we can obtain the classification of all solutions to. (2014) Classification of All Single Traveling Wave Solutions to (3 + 1)-Dimensional Breaking Soliton Equation. We take into account (3 + 1)-dimensional breaking soliton equation, and it reads as uxxt + auxxxuyz + buxxyuxz + cuxyuxxz + duxxuxyz + euxxxyz = 0. Shi [8] gave some exact solutions of Equation (2) by turning it into KdV equation though introducing a simple transformation, and so on

Classification

Conclusion