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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 goveing 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.