Solitons, peakons, and periodic cuspons of a generalized Degasperis-Procesi equation

Details Solitons, peakons, and periodic cuspons of a generalized Degasperis-Procesi equation Solitons, peakons, and periodic cuspons of a generalized Degasperis-Procesi equation

2009-08-06

arxiv.org/abs/0908.0905v1

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

Nonlinear Sciences

Pattern Formation and Solitons

14 pages, 41 figures

Scientific paper

10.1155/2009/249361

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 reasonwhy these solutions can exist in this equation are also given.

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