Modulational instability of dust-acoustic and dust-ion-acoustic waves

Using the standard reductive perturbation technique, a nonlinear Schr\"odinger 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.