SINGULAR PERIODIC WAVES OF AN INTEGRABLE EQUATION FROM SHORT CAPILLARY-GRAVITY WAVES | Zendy

Chunhai Li | Zendy; Shengqiang Tang | Zendy; Wentao Huang | Zendy; Feng Zhao | Zendy

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SINGULAR PERIODIC WAVES OF AN INTEGRABLE EQUATION FROM SHORT CAPILLARY-GRAVITY WAVES

Author(s) -

Chunhai Li,

Shengqiang Tang,

Wentao Huang,

Feng Zhao

Publication year - 2017

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2017063

Subject(s) - peakon , integrable system , mathematical analysis , parabola , mathematics , singularity , sinusoidal plane wave solutions of the electromagnetic wave equation , physics , singular solution , classical mechanics , geometry , electromagnetic wave equation , quantum mechanics , magnetic field , optical field

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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