Nonlinear Phenomena in Complex Systems, 2019, Vol.22, No.3, pp.242

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2019, Vol.22, No.3, pp.242 - 250

Dynamics of Distorted Solitons in the Modified Zakharov-Kuznetsov Model
G. A. Omel'yanov and G. A. Orozco-Casillas

We consider 1 + 2-dimensional Zakharov-Kuznetsov type equation with nonlinearity u^κ, κ > 1, and with small dispersion ε. The main result consists in the construction of the soliton type asymptotics which describes the influence of long wave perturbations of the initial wave front and amplitude. It turned out that the correctness condition for the asymptotic solution is similar to the stability condition known for the case of small perturbations of the classical ZK equation. Results of numerical simulations are presented.

Key words: modified Zakharov-Kuznetsov equation, soliton, perturbation, stability

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