Nonlinear low-frequency waves in dusty self-gravitating plasmas

Nonlinear electrostatic waves in self-gravitating dusty plasmas are considered in two limiting cases, according to whether the charged-particle dynamics is governed mostly by electrostatic forces or mostly by gravitation. This shows a significant difference between these two plasma media with respect to the envelope dynamics in the nonlinear regime. In the former case, when omega (2)(p alpha) > omega (2)(J alpha), the amplitude perturbations are longitudinally unstable only in the short-wave range, and the nonlinear effects can result in the formation of longitudinal dust-acoustic solitary waves. But even weak self-gravitation prevents the formation of dust-acoustic solitons, and only transverse solitary structures are possible. In the other limiting case (omega (2)(p alpha) < <omega>(2)(J alpha)), there is always a transverse modulational instability, which can lead to transverse solitary waves. In both cases, there is a threshold for solitary-wave formation.