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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 183159, 14 pages
Research Article

Bifurcations and Parametric Representations of Peakon, Solitary Wave and Smooth Periodic Wave Solutions for a Two-Component Degasperis-Procesi Equation

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

Received 27 May 2013; Revised 26 July 2013; Accepted 26 July 2013

Academic Editor: Jingxin Zhang

Copyright © 2013 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.


By using the bifurcation method of dynamical systems and the method of phase portraits analysis, we consider a two-component Degasperis-Procesi equation: , , the existence of the peakon, solitary wave and smooth periodic wave is proved, and exact parametric representations of above travelling wave solutions are obtained in different parameter regions.