M-Shape peakons, dehisced solitons, cuspons and new 1-peak solitons for the Degasperis–Procesi equation

Zhijun Qiao

Chaos, Solitons & Fractals, 2008, vol. 37, issue 2, 501-507

Abstract: In this paper, we investigate all possible single traveling solitary wave solutions of the Degasperis–Procesi (DP) equation under the boundary condition u→A (A is a constant) as x→±∞. Regular peakons of the DP equation correspond to the case of A=0. In the case of A≠0, we find new exact soliton solutions including cuspon, peakon, M-shape peakon, dehisced soliton, and double dehisced 1-peak soliton. In particular, we propose three new types of soliton solutions – M-shape peakon, dehisced soliton, and double dehisced 1-peak soliton, which are given in an explicit form. The most interesting is: for the DP equation the cuspon is a limit of those new peaked solutions solutions. We show some graphs to explain our new solutions.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:37:y:2008:i:2:p:501-507

DOI: 10.1016/j.chaos.2006.09.092

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