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

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  • Qiao, Zhijun

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.

Suggested Citation

  • Qiao, Zhijun, 2008. "M-Shape peakons, dehisced solitons, cuspons and new 1-peak solitons for the Degasperis–Procesi equation," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 501-507.
    • Handle: RePEc:eee:chsofr:v:37:y:2008:i:2:p:501-507
    DOI: 10.1016/j.chaos.2006.09.092
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    1. Qiao, Zhijun & Qiao, Xin Brian, 2005. "Cusp solitons and cusp-like singular solutions for nonlinear equations," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 153-163.
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    Cited by:

    1. Rodriguez, J. Noyola & Omel’yanov, G., 2019. "General Degasperis-Procesi equation and its solitary wave solutions," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 41-46.

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