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

Abstract EN

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.