Cusp solitons and cusp-like singular solutions for nonlinear equations

Zhijun Qiao and Xin Brian Qiao

Chaos, Solitons & Fractals, 2005, vol. 25, issue 1, 153-163

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.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:25:y:2005:i:1:p:153-163

DOI: 10.1016/j.chaos.2004.09.074

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