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Abstract and Applied Analysis
Volume 2015 (2015), Article ID 369294, 7 pages
Research Article

Classification of Multiply Travelling Wave Solutions for Coupled Burgers, Combined KdV-Modified KdV, and Schrödinger-KdV Equations

1Mathematics Department, Faculty of Science, Taibah University, Al-Ula, Saudi Arabia
2Mathematics Department, Faculty of Science, Beni-Suef University, Egypt
3Mathematics Department, College of Arts and Science, Taif University, Ranyah, Saudi Arabia

Received 24 August 2014; Accepted 1 November 2014

Academic Editor: Yasir Khan

Copyright © 2015 A. R. Seadawy and K. El-Rashidy. 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.


Some explicit travelling wave solutions to constructing exact solutions of nonlinear partial differential equations of mathematical physics are presented. By applying a theory of Frobenius decompositions and, more precisely, by using a transformation method to the coupled Burgers, combined Korteweg-de Vries- (KdV-) modified KdV and Schrödinger-KdV equation is written as bilinear ordinary differential equations and two solutions to describing nonlinear interaction of travelling waves are generated. The properties of the multiple travelling wave solutions are shown by some figures. All solutions are stable and have applications in physics.