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Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 153974, 8 pages
http://dx.doi.org/10.1155/2014/153974
Research Article

Exp-Function Method for a Generalized MKdV Equation

School of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China

Received 15 December 2013; Accepted 24 April 2014; Published 15 May 2014

Academic Editor: Cengiz Çinar

Copyright © 2014 Yuzhen Chai 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.

Abstract

Under investigation in this paper is a generalized MKdV equation, which describes the propagation of shallow water in fluid mechanics. In this paper, we have derived the exact solutions for the generalized MKdV equation including the bright soliton, dark soliton, two-peak bright soliton, two-peak dark soliton, shock soliton and periodic wave solution via Exp-function method. By figures and symbolic computations, we have discussed the propagation characteristics of those solitons under different values of those coefficients in the generalized MKdV equation. The method constructing soliton solutions in this paper may be useful for the investigations on the other nonlinear mathematical physics model and the conclusions of this paper can give theory support for the study of dynamic features of models in the shallow water.