  Theoretical and numerical studies are presented of the nonlinear amplitude
modulation of dust-acoustic (DA) waves propagating in an unmagnetized three
component, weakly-coupled, fully ionized plasma consisting of electrons,
positive ions and charged dust particles, considering perturbations oblique to
the carrier wave propagation direction. The stability analysis, based on a
nonlinear Schroedinger-type equation (NLSE), shows that the wave may become
unstable; the stability criteria depend on the angle $\theta$ between the
modulation and propagation directions. Explicit expressions for the instability
rate and threshold have been obtained in terms of the dispersion laws of the
system. The possibility and conditions for the existence of different types of
localized excitations have also been discussed.
