Exact Traveling Wave Solutions of Nonlinear PDEs in Mathematical Physics

J F Alzaidy

doi:10.4236/am.2012.37109

Abstract

In the present article, we construct the exact traveling wave solutions of nonlinear PDEs in mathematical physics via the variant Boussinesq equations and the coupled KdV equations by using the extended mapping method and auxiliary equation method. This method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear partial differential equations arising in mathematical physics.

Highlights

We construct the exact traveling wave solutions of nonlinear PDEs in mathematical physics via the variant Boussinesq equations and the coupled KdV equations by using the extended mapping method and auxiliary equation method. This method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear partial differential equations arising in mathematical physics
The effort in finding exact solutions to nonlinear equations is important for the understanding of most nonlinear physical phenomena
The nonlinear wave phenomena observed in fluid dynamics, plasma and optical fibers are often modeled by the bell shaped sech solutions and the kink shaped tanh solutions

Summary

Introduction

The effort in finding exact solutions to nonlinear equations is important for the understanding of most nonlinear physical phenomena. The nonlinear wave phenomena observed in fluid dynamics, plasma and optical fibers are often modeled by the bell shaped sech solutions and the kink shaped tanh solutions. The main objective of this paper is used the extended mapping method and auxiliary equation method to construct the exact solutions for nonlinear evolution equations in the mathematical physics via the variant Boussinesq equations and the coupled KdV equations. Under the transformation (2), Equation (1) becomes an ordinary differential equation (ODE) as

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Methods

Conclusion