Shock waves in a strongly coupled inhomogeneous dusty plasma

Abstract

Nonlinear theory for certain dust acoustic waves has been developed for a strongly coupled inhomogeneous collisionless dusty plasma containing dust particles of different sizes. The generalized hydrodynamic set of partial differential equations is considered to describe the fluid model of the present nonlinear system. A reductive perturbation technique is employed on this nonlinear set of equations to derive a variable coefficient Korteweg-deVries (KdV)–Burgers equation with a forcing term. The generalized expansion method is performed to obtain an analytic expression for the solution. This analytic solution describes the monotonic kink-type shock waves, due to the dominant nature of the dissipation term over the dispersion term. In addition to the effects of inhomogeneity and grain size distribution, the effects of nonthermal ions, dust–dust correlation and ion temperature on the wave propagation are investigated. Also, a steady-state monotonic shock solution of the KdV-Burgers equation is obtained numerically. The obtained results are discussed in the context of some dusty plasmas, previously reported experimentally or theoretically.