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Mathematical Problems in Engineering
Volume 2014, Article ID 746538, 20 pages
Research Article

The -Expansion Method and Its Applications for Solving Two Higher Order Nonlinear Evolution Equations

Department of Mathematics, Faculty of Science, Zagazig University, P.O. Box 44519, Zagazig, Egypt

Received 19 March 2014; Accepted 23 April 2014; Published 17 June 2014

Academic Editor: Oded Gottlieb

Copyright © 2014 E. M. E. Zayed and K. A. E. Alurrfi. 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.


The two variable -expansion method is employed to construct exact traveling wave solutions with parameters of two higher order nonlinear evolution equations, namely, the nonlinear Klein-Gordon equations and the nonlinear Pochhammer-Chree equations. When the parameters are replaced by special values, the well-known solitary wave solutions of these equations are rediscovered from the traveling waves. This method can be thought of as the generalization of well-known original -expansion method proposed by Wang et al. It is shown that the two variable -expansion method provides a more powerful mathematical tool for solving many other nonlinear PDEs in mathematical physics.