Nonlinear dust acoustic waves in magnetized two-ion-temperature dusty plasmas

A Zakharov-Kuznetsov (ZK) equation, a modified ZK equation and a coupled ZK equation for small but finite amplitude dust acoustic waves in a magnetized two-ion-temperature dusty plasma with dust size distribution have been obtained in this paper. It seems that the soliton velocity for a dusty plasma with power law dust size distribution is larger than that of monosized dusty plasmas. The solitary waves with opposite polarity particles are investigated as well. It is found that rarefactive and compressive solitary waves exist in this system which depend on different conditions. On the other hand, the solitary wave is unstable at certain regions when the wave numbers of the transverse perturbations satisfies the conditions of 0