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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 462957, 7 pages
http://dx.doi.org/10.1155/2013/462957
Research Article

Existence Analysis of Traveling Wave Solutions for a Generalization of KdV Equation

College of Mathematics, Honghe University, Mengzi, Yunnan 661100, China

Received 12 September 2012; Accepted 16 November 2012

Academic Editor: Salvatore Alfonzetti

Copyright © 2013 Yao Long and Can Chen. 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

By using the bifurcation theory of dynamic system, a generalization of KdV equation was studied. According to the analysis of the phase portraits, the existence of solitary wave, cusp wave, periodic wave, periodic cusp wave, and compactons were discussed. In some parametric conditions, exact traveling wave solutions of this generalization of the KdV equation, which are different from those exact solutions in existing references, were given.