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Cusp solitons and cusp-like singular solutions for nonlinear equations

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  • Qiao, Zhijun
  • Qiao, Xin Brian

Abstract

This paper gives two new families of nonlinear partial differential equations (PDEs). One has cusp soliton solution while the other possesses the cusp-like singular traveling wave solution. A typical integrable system: Harry–Dym (HD) equation is able to be contained in both families and has cusp soliton solution as well as cusp-like singular traveling wave solution. We prove that the cusp solution of the HD equation is not stable and the cusp-like solution is not included in the parametric solutions of the HD equation.

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  • 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.
    • Handle: RePEc:eee:chsofr:v:25:y:2005:i:1:p:153-163
    DOI: 10.1016/j.chaos.2004.09.074
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    Cited by:

    1. 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.

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