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Journal of Applied Mathematics
Volume 2014, Article ID 839485, 11 pages
Research Article

Stability Analysis for Travelling Wave Solutions of the Olver and Fifth-Order KdV Equations

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

Received 8 November 2013; Revised 25 January 2014; Accepted 2 February 2014; Published 24 March 2014

Academic Editor: Michael Meylan

Copyright © 2014 A. R. Seadawy et al. 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 Olver equation is governing a unidirectional model for describing long and small amplitude waves in shallow water waves. The solitary wave solutions of the Olver and fifth-order KdV equations can be obtained by using extended tanh and sech-tanh methods. The present results are describing the generation and evolution of such waves, their interactions, and their stability. Moreover, the methods can be applied to a wide class of nonlinear evolution equations. All solutions are exact and stable and have applications in physics.