Applications of an Extended -Expansion Method to Find Exact Solutions of Nonlinear PDEs in Mathematical Physics

Author:

Zayed E. M. E.12ORCID,Al-Joudi Shorog2ORCID

Affiliation:

1. Mathematics Department, Faculty o f Science, Zagazig University, Zagazig, Egypt

2. Mathematics Department, Faculty o f Science, Taif University, P.O. Box 888, El-Taif, Saudi Arabia

Abstract

We construct the traveling wave solutions of the (1+1)-dimensional modified Benjamin-Bona-Mahony equation, the (2+1)-dimensional typical breaking soliton equation, the (1+1)-dimensional classical Boussinesq equations, and the (2+1)-dimensional Broer-Kaup-Kuperschmidt equations by using an extended -expansion method, whereGsatisfies the second-order linear ordinary differential equation. By using this method, new exact solutions involving parameters, expressed by three types of functions which are hyperbolic, trigonometric and rational function solutions, are obtained. When the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions.

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

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