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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 926838, 7 pages
Research Article

Traveling Wave Solutions of the Benjamin-Bona-Mahony Water Wave Equations

1Mathematics Department, Faculty of Science, Taibah University, Al-Ula 41921-259, Saudi Arabia
2Mathematics Department, Faculty of Science, Beni-Suef University, Egypt

Received 5 August 2014; Revised 1 September 2014; Accepted 4 September 2014; Published 15 October 2014

Academic Editor: Santanu Saha Ray

Copyright © 2014 A. R. Seadawy and A. Sayed. 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 modeling of unidirectional propagation of long water waves in dispersive media is presented. The Korteweg-de Vries (KdV) and Benjamin-Bona-Mahony (BBM) equations are derived from water waves models. New traveling solutions of the KdV and BBM equations are obtained by implementing the extended direct algebraic and extended sech-tanh methods. The stability of the obtained traveling solutions is analyzed and discussed.