Bifurcations of traveling wave solutions for an integrable equation | Zendy

Jibin Li | Zendy; Zhijun Qiao | Zendy

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Bifurcations of traveling wave solutions for an integrable equation

Author(s) -

Jibin Li,

Zhijun Qiao

Publication year - 2010

Publication title -

journal of mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.708

H-Index - 119

eISSN - 1089-7658

pISSN - 0022-2488

DOI - 10.1063/1.3385777

Subject(s) - traveling wave , integrable system , mathematical analysis , periodic wave , wave equation , parametric statistics , sinusoidal plane wave solutions of the electromagnetic wave equation , bounded function , physics , mathematics , mathematical physics , quantum mechanics , electromagnetic wave equation , statistics , magnetic field , optical field

This paper deals with the following equation m t=(1/2)(1/m k) xxx-(1/2)(1/m k) x, which is proposed by Z. J. Qiao [J. Math. Phys.48, 082701 (2007)] and Qiao and Liu [Chaos, Solitons Fractals41, 587 (2009)]. By adopting the phase analysis method of planar dynamical systems and the theory of the singular traveling wave systems to the traveling wave solutions of the equation, it is shown that for different k, the equation may have infinitely many solitary wave solutions, periodic wave solutions, kink/antikink wave solutions, cusped solitary wave solutions, and breaking loop solutions. We discuss in a detail the cases of k=-2,-1/2,1/2,2, and parametric representations of all possible bounded traveling wave solutions are given in the different (c,g)-parameter regions. © 2010 American Institute of Physics.

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