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.
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Duan Wen-Shan (2002) studied this question.
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