Advances in Mathematical Physics (Jan 2013)

Bifurcation Phenomena of Nonlinear Waves in a Generalized Zakharov-Kuznetsov Equation

  • Yun Wu,
  • Zhengrong Liu

DOI
https://doi.org/10.1155/2013/812120
Journal volume & issue
Vol. 2013

Abstract

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We study the bifurcation phenomena of nonlinear waves described by a generalized Zakharov-Kuznetsov equation ut+au2+bu4ux+γuxxx+δuxyy=0. We reveal four kinds of interesting bifurcation phenomena. The first kind is that the low-kink waves can be bifurcated from the symmetric solitary waves, the 1-blow-up waves, the tall-kink waves, and the antisymmetric solitary waves. The second kind is that the 1-blow-up waves can be bifurcated from the periodic-blow-up waves, the symmetric solitary waves, and the 2-blow-up waves. The third kind is that the periodic-blow-up waves can be bifurcated from the symmetric periodic waves. The fourth kind is that the tall-kink waves can be bifurcated from the symmetric periodic waves.