Dynamics of Distorted Solitons in the Modified Zakharov–Kuznetsov Model

Abstract

We consider 1 + 2-dimensional Zakharov-Kuznetsov type equation with nonlinearity uκ, 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.