International Journal of Differential Equations
Volume 2011 (2011), Article ID 582512, 16 pages
http://dx.doi.org/10.1155/2011/582512
Research Article

Periodic and Solitary-Wave Solutions for a Variant of the 𝐾 ( 3 , 2 ) Equation

Jiangbo Zhou and Lixin Tian

Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China

Received 5 May 2011; Accepted 16 August 2011

Academic Editor: Mayer Humi

Copyright © 2011 Jiangbo Zhou and Lixin Tian. 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 employ the bifurcation method of planar dynamical systems and qualitative theory of polynomial differential systems to derive new bounded traveling-wave solutions for a variant of the 𝐾 ( 3 , 2 ) equation. For the focusing branch, we obtain hump-shaped and valley-shaped solitary-wave solutions and some periodic solutions. For the defocusing branch, the nonexistence of solitary traveling wave solutions is shown. Meanwhile, some periodic solutions are also obtained. The results presented in this paper supplement the previous results.