The Zakharov–Kuznetsov equation for nonlinear ion-acoustic waves

Abstract

The Zakharov-Kuznetsov equation is used to describe ion-acoustic wave propagation in a magnetic environment. An initial-value problem is solved for this equation on the basis of a numerical method that uses the fast-Fourier-transform technique for calculating space derivatives and a fourth-order Runge-Kutta method for the time scheme. Numerical simulations show that the disturbed flat (planar) solitary waves can break up into more robust cylindrical ones. Interactions between these two types of wave, and recurrence phenomena, are also studied.