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Journal of Applied Mathematics
Volume 2012, Article ID 236875, 23 pages
http://dx.doi.org/10.1155/2012/236875
Research Article

Exact Traveling Wave Solutions of Explicit Type, Implicit Type, and Parametric Type for K(m,n) Equation

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 9 December 2011; Accepted 22 January 2012

Academic Editor: J. Biazar

Copyright © 2012 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

By using the integral bifurcation method, we study the nonlinear K(m,n) equation for all possible values of m and n. Some new exact traveling wave solutions of explicit type, implicit type, and parametric type are obtained. These exact solutions include peculiar compacton solutions, singular periodic wave solutions, compacton-like periodic wave solutions, periodic blowup solutions, smooth soliton solutions, and kink and antikink wave solutions. The great parts of them are different from the results in existing references. In order to show their dynamic profiles intuitively, the solutions of K(n,n), K(2n1,n), K(3n2,n), K(4n3,n), and K(m,1) equations are chosen to illustrate with the concrete features.