Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 249361, 13 pages
Research Article

Solitons, Peakons, and Periodic Cuspons of a Generalized Degasperis-Procesi Equation

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

Received 24 November 2008; Accepted 23 February 2009

Academic Editor: Elbert E. Neher Macau

Copyright © 2009 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.


We employ the bifurcation theory of planar dynamical systems to investigate the exact travelling wave solutions of a generalized Degasperis-Procesi equation utuxxt+4uux+γ(uuxx)x=3uxuxx+uuxxx. The implicit expression of smooth soliton solutions is given. The explicit expressions of peaked soliton solutions and periodic cuspon solutions are also obtained. Further, we show the relationship among the smooth soliton solutions, the peaked soliton solutions, and the periodic cuspon solutions. The physical relevance of the found solutions and the reason why these solutions can exist in this equation are also given.