Volume 2, Issue 1

(4)Traveling wave solutions for shallow water equations

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U.M. Abdelsalam
Department of Mathematics, Faculty of Science, Fayoum University, Al Fayoum, Egypt

Received 15 November 2016; received in revised form 6 January 2017; accepted 6 February 2017
Available online 14 February 2017

Abstract
An extended homogeneous balance method is suggested in this paper. Based on computerized symbolic computation and the homogeneous balance method, new exact traveling wave solutions of nonlinear partial differential equations (PDEs) are presented. The shallow-water equations represent a simple yet realistic set of equations typically found in atmospheric or ocean modeling applications, we consider the exact solutions of the nonlinear generalized shallow water equation and the fourth order Boussinesq equation. Applying this method, with the aid of Mathematica, many new exact traveling wave solutions are successfully obtained.
© 2017 Shanghai Jiaotong University. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license. (
http://creativecommons.org/licenses/by-nc-nd/4.0/ )
 

Keywords: Extended homogeneous balance method; Shallow water equation; Boussinesq equation; Traveling wave solutions.