The Investigation of Exact Solutions for the Appropriate Type of the Dispersive Long Wave Equation

J Biazar,Z Salehdirin,M B Mehrlatifan

doi:10.1155/2014/967176

Abstract

Improved (G'/G)-expansion and first integral methods are used to construct exact solutions of the 2+1-dimensional Eckhaus-type extension of the dispersive long wave equation. The (G'/G)-expansion method is based on the assumptions that the travelling wave solutions can be expressed by a polynomial in (G'/G) and the first integral method is based on the theory of commutative algebra in which Division Theorem is of concern. It is worth mentioning that these methods are used for different systems and those two different systems can both be reduced to a system that will be mentioned in this paper. To recapitulate, this investigation has resulted in the exact solutions of the given systems.

Highlights

The investigation of exact solutions to nonlinear evolution has become an interesting subject in nonlinear science field, since the time when the soliton concept was first introduced by Zabusky and Kruskal in 1965 [1]
Two different methods in this study have been employed to result in the exact solutions of the given systems
The transformation of the obtained solutions has been defined in order to gain the exact solutions in which some of them are soliton

Summary

Introduction

The investigation of exact solutions to nonlinear evolution has become an interesting subject in nonlinear science field, since the time when the soliton concept was first introduced by Zabusky and Kruskal in 1965 [1]. It was not until the mid1960s when applied scientists began to use modern digital computers to study nonlinear wave propagation that the soundness of Russell’s early ideas began to be appreciated. He viewed the solitary wave as a self-sufficient dynamic entity; a “thing” displaying many properties of a particle. The aim of this paper is to find exact solutions of the (2 + 1)-dimensional Eckhaus-type (2) and (3) by various methods

Methodology

Application

Conflict of Interests

Conclusion