Adiabatic dust-acoustic waves with dust-charge fluctuations

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 uni directional propagation, the Boussinesq-like equation reduces to usual Kortewegde 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.