Nonlinear waves and structures in dusty plasmas

Recent laboratory observations conclusively reveal that coherent nonlinear waves and structures (viz., solitons, shocks, Mach cones, voids, vortices, etc.) can be produced in a dusty plasma. Our objective here is to describe the underlying physics, mathematical details, and salient features of dust ion-acoustic as well as dust acoustic solitary and shock waves, dust voids, and dust vortex flows. It is shown that the presence of charged dust grains introduces new features to the nonlinear electrostatic waves and structures. Consideration of the dust charge fluctuation dynamics causes a novel dissipation, which is responsible for the formation of dust ion-acoustic shock waves. Furthermore, the formation of a dust void is associated with double layers and ion holes arising from trapped ion effects. Finally, a nonlinear model for dust vortex flows is presented. It is shown that the dynamics of dust vortex flows in a plasma is governed by a modified Navier-Stokes equation (MNSE), and that possible stationary solutions of the MNSE can be represented as monopolar as well as a row of identical and a row of counter-rotating vortices. The implications of our theoretical results/models to experimental observations of solitary and shock waves as well as of voids and vortices are discussed. (C) 2003 American Institute of Physics.