Stability of Dust Acoustic Waves in Weakly Two-Dimensional Dust Plasma with Vortex-Like Ion Distribution

By considering the vortex-like ion distribution, we know that the nonlinear dust acoustic wave can be described by the modified Korteweg-de Vries equation. If there are high-order transverse perturbations in this system, the governing equation for this system is the modified Kadomtsev-Petviashvili equation. We also find that for this system under the transverse perturbation the one-dimensional solitary wave solution is stable.