Abstract and Applied Analysis
Volume 2013 (2013), Article ID 656297, 15 pages
http://dx.doi.org/10.1155/2013/656297
Research Article

A Generalized KdV Equation of Neglecting the Highest-Order Infinitesimal Term and Its Exact Traveling Wave Solutions

Xianbin Wu,1 Weiguo Rui,2 and Xiaochun Hong3

1Junior College, Zhejiang Wanli University, Ningbo 315100, China
2College of Mathematics, Honghe University, Mengzi, Yunnan 661100, China
3College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China

Received 3 November 2012; Accepted 15 January 2013

Academic Editor: Julian López-Gómez

Copyright © 2013 Xianbin Wu 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

We study a generalized KdV equation of neglecting the highest order infinitesimal term, which is an important water wave model. Some exact traveling wave solutions such as singular solitary wave solutions, semiloop soliton solutions, dark soliton solutions, dark peakon solutions, dark loop-soliton solutions, broken loop-soliton solutions, broken wave solutions of U-form and C-form, periodic wave solutions of singular type, and broken wave solution of semiparabola form are obtained. By using mathematical software Maple, we show their profiles and discuss their dynamic properties. Investigating these properties, we find that the waveforms of some traveling wave solutions vary with changes of certain parameters.