Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 320163, 10 pages
http://dx.doi.org/10.1155/2012/320163
Research Article

Periodic Loop Solutions and Their Limit Forms for the Kudryashov-Sinelshchikov Equation

Bin He,1 Qing Meng,2 Jinhua Zhang,1 and Yao Long1

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

Received 5 December 2011; Revised 24 January 2012; Accepted 30 January 2012

Academic Editor: Stefano Lenci

Copyright © 2012 Bin He 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

The Kudryashov-Sinelshchikov equation is studied by using the bifurcation method of dynamical systems and the method of phase portraits analysis. We show that the limit forms of periodic loop solutions contain loop soliton solutions, smooth periodic wave solutions, and periodic cusp wave solutions. Also, some new exact travelling wave solutions are presented through some special phase orbits.