Nonlinear adiabatic models of ion-acoustic waves in dust plasma

Nonlinear adiabatic models of ion-acoustic waves in a dust plasma are developed. The problem of the structure of subsonic periodic and supersonic solitary ion-acoustic waves is exactly solved analytically under the assumption of a constant charge of dust particles; the critical Mach numbers for the solitary wave are determined. The problem of the wave structure is solved numerically for the case when the charge of dust particles was assumed to be variable.