Modulational instability and localized excitations of dust-ion acoustic waves

Theoretical and numerical studies are carried out of the nonlinear amplitude modulation of dust-ion acoustic waves propagating in an unmagnetized weakly coupled plasma comprised of electrons, positive ions, and charged dust grains, considering perturbations oblique to the carrier wave propagation direction. The stability analysis, based on a nonlinear Schrödinger-type equation, exhibits a wide instability region, which depends on both the angle θ between the modulation and propagation directions and the dust number density nd. Explicit expressions for the instability increment and threshold are obtained. The possibility and conditions for the existence of different types of localized excitations are also discussed.