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