A New Method with a Different Auxiliary Equation to Obtain Solitary Wave Solutions for Nonlinear Partial Differential Equations

Bülent Kiliç,Hasan Bulut

doi:10.1155/2013/890784

Abstract

A new method with a different auxiliary equation from the Riccati equation is used for constructing exact travelling wave solutions of nonlinear partial differential equations. The main idea of this method is to take full advantage of a different auxilliary equation from the Riccati equation which has more new solutions. More new solitary solutions are obtained for the RLW Burgers and Hirota Satsuma coupled equations.

Highlights

Remarkable progress has been made in the construction of the exact solutions for nonlinear partial differential equations, which have been a basic concern for both mathematicians and physicists [1–3].We do not attempt to characterize the general form of nonlinear dispersive wave equations [4, 5]
The fact that the solutions of many nonlinear equations can be expressed as a finite series of solutions of the auxiliary equation motivates us to seek for the solutions of (1) in the form m u (x, t) = λ∑ [ai F(ξ)i + a−i F(ξ)−i ], (2)
We have presented a new method and balance term definition and used it to solve the RLW Burgers and Hirota Satsuma coupled equations

Summary

Introduction

Remarkable progress has been made in the construction of the exact solutions for nonlinear partial differential equations, which have been a basic concern for both mathematicians and physicists [1–3].We do not attempt to characterize the general form of nonlinear dispersive wave equations [4, 5]. The studies in finding exact solutions to nonlinear differential equation (NPDE), when they exist, are very important for the understanding of most nonlinear physical phenomena. There are many studies which obtain explicit solutions for nonlinear differential equations. Many explicit exact methods have been introduced in literature [7–21]. In the second section contains analyze of a new method and balance term definition. We will obtain wave solutions of RLW Burgers and Hirota Satsuma coupled equations by using a new method.

Method and Its Applications

Application of the Method

Conclusion