For dust acoustic waves in unmagnetized plasma comprising cold dust grains
and both isothermal electrons and ions, small but finite amplitude nonlinea
r waves are governed by the Korteweg-de Vries equation. The weakly transver
se long wavelength perturbations for nonlinear dust acoustic waves are inve
stigated in this paper. It has been shown that the governing equation for t
his process is the Kadomtsev-Petviashvili equation. It suggests that the tr
ansverse perturbations for the nonlinear acoustic solitary waves in a dusty
plasma are stable. (C) 2001 American Institute of Physics.