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Discrete Dynamics in Nature and Society
Volume 2016, Article ID 5383527, 15 pages
http://dx.doi.org/10.1155/2016/5383527
Research Article

Bounded Traveling Wave Solutions and Their Relations for the Generalized HD Type Equation

1Department of Physics, Honghe University, Mengzi, Yunnan 661100, China
2College of Mathematics, Honghe University, Mengzi, Yunnan 661100, China

Received 17 March 2016; Revised 18 June 2016; Accepted 4 July 2016

Academic Editor: Andrew Pickering

Copyright © 2016 Qing Meng and Bin He. 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

The generalized HD type equation is studied by using the bifurcation method of dynamical systems. From a dynamic point of view, the existence of different kinds of traveling waves which include periodic loop soliton, periodic cusp wave, smooth periodic wave, loop soliton, cuspon, smooth solitary wave, and kink-like wave is proved and the sufficient conditions to guarantee the existence of the above solutions in different regions of the parametric space are given. Also, all possible exact parametric representations of the bounded waves are presented and their relations are stated.