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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 521712, 10 pages
http://dx.doi.org/10.1155/2014/521712
Research Article

The ( )-Expansion Method and Its Applications to Find the Exact Solutions of Nonlinear PDEs for Nanobiosciences

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

Received 14 November 2013; Accepted 10 February 2014; Published 25 March 2014

Academic Editor: Elmetwally Elabbasy

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.

Abstract

The two-variable ( )-expansion method is employed to construct exact traveling wave solutions with parameters of nanobiosciences partial differential equation. When the parameters are replaced by special values, the solitary wave solutions and the periodic wave solutions of this equation have been obtained from the traveling waves. This method can be thought of as the generalization of well-known original -expansion method proposed by M. 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. Comparison between our results and the well-known results is given.