We study the effect of charge fluctuations on the propagation of
adiabatic linear
and nonlinear dust-acoustic waves by considering the electrons and ions
to be in
Boltzmann equilibria, and the dust grains to satisfy the fluid equations
with full
adiabatic equation of state. Linear dust-acoustic waves are damped owing
to the
dust-charge fluctuations, and the damping rate decreases with increasing
adiabatic
dust pressure. Nonlinear dust-acoustic waves are governed by the set of
coupled
Boussinesq-like and dust-charge perturbation equations. It is shown that
for unidirectional
propagation, the Boussinesq-like equation reduces to usual Korteweg–de
Vries
(KdV) equation. At early times, the localized solutions of the KdV equation
are damped owing to the dust-charge perturbations. The soliton amplitude
decreases with increasing adiabatic dust plasma pressure and increases
with Mach
number. Soliton solutions are found only in the supersonic regime.
