Instability of Waves in Magnetized Vortex-Like Ion Distribution Dusty Plasmas

A modified Zakharov-Kuznetsov equation for small but finite amplitude dust acoustic waves in a magnetized vortex-like ion distribution dusty plasma is obtained in this paper. It seems that there are instability for a soliton under higher-order transverse perturbations in this system. There is a certain critical value 4λ0. If the ratio of the wave length of the higher-order perturbations to the width of the soliton is larger than this critical value, the solitary wave is unstable, otherwise it is stable.