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 ω2pα > ω2Jα, 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-gravitational effects can lead to the existence
of a long-wavelength range, where self-gravitation prevents the formation of dust-acoustic
solitons, and only transverse solitary structures are possible. In the other
limiting case (ω2pα < ω2Jα), 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.