Effect of Weakly Transverse Perturbations on Dust Acoustic Solitary Waves with Adiabatic Variation of Dust Charge

By employing the reductive perturbation technique we derived a Kadomtsev-Petviashvili equation for unmagnetized dusty plasmas. It suggests that the nonlinear dust acoustic solitary waves with adiabatic variation of dust charge are stable even there are some higher order transverse perturbatoins. There are only rarefactive solitary waves for this system which has been verified analytically in this paper.