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Volume 7, Number 3, 2017, Pages 1013-1021                                                                DOI:10.11948/2017063
Singular periodic waves of an integrable equation from short capillary-gravity waves
Chunhai Li,Shengqiang Tang,Wentao Huang,Feng Zhao
Keywords:Bifurcation theory of dynamical systems, peakon, periodic peakon, periodic wave, parabola singular curve.
      The effects of parabola singular curves in the integrable nonlinear wave equation are studied by using the bifurcation theory of dynamical system. We find new singular periodic waves for a nonlinear wave equation from short capillary-gravity waves. The new periodic waves possess weaker singularity than the periodic peakon. It is shown that the second derivatives of the new singular periodic wave solutions do not exist in countable number of points but the first derivatives exist. We show that there exist close connection between the new singular periodic waves and parabola singular curve in phase plane of traveling wave system for the first time.
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