Using the standard reductive perturbation technique, a nonlinear Schrödinger equation is derived to study the modulational instability of finite amplitude dust-acoustic (DA) and dust-ion-acoustic (DIA) waves against oblique perturbations (with respect to the propagation direction of the carrier waves) in an unmagnetized dusty plasma. It is shown that both the DA and DIA waves are modulationally unstable. Possible stationary states of the wave packets can appear as envelope solitons.

• Received 2 February 1998

DOI:https://doi.org/10.1103/PhysRevE.58.6517