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Mathematical Problems in Engineering
Volume 2010, Article ID 768573, 19 pages
Research Article

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

1Mathematics Department, Faculty o f Science, Zagazig University, Zagazig, Egypt
2Mathematics Department, Faculty o f Science, Taif University, P.O. Box 888, El-Taif, Saudi Arabia

Received 10 December 2009; Accepted 16 June 2010

Academic Editor: Gradimir V. Milovanović

Copyright © 2010 E. M. E. Zayed and Shorog Al-Joudi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 ( 𝐺 / 𝐺 ) -expansion method, where G satisfies 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.