Damped Korteweg–de Vries equation in a fluid-kinetic model for dusty plasmas

A hybrid fluid-kinetic (statistical mechanical) approach is adopted to model the dynamics of solitary waves representing collective ion excitations in a plasma contaminated with massive charged dust particulates. The ion component is modeled by fluid-dynamical equations, while the background electron population is modeled by a statistical–mechanical (i.e., kinetic) formalism. A multi-scale (reductive perturbation) technique reduces the fluid-kinetic formulation to a modified Korteweg–de Vries (KdV) equation, incorporating an additional term associated to kinetic effects, leading to wave damping. Our aim is to trace the combined influence of the charged dust concentration on the collisionless kinetic damping (known as Landau damping) mechanism affecting electrostatic waves propagating in a plasma contaminated by charged dust particulates (commonly referred to as a dusty plasma). A kappa-type distribution is assumed for the electrons, in agreement with Space observations. As a striking new aspect in this study, solitary wave polarity reversal is predicted when the dust concentration exceeds a certain threshold; this is true regardless of the kappa parameter value. The dependence of the damped solitary wave propagation characteristics on the (non-Maxwellian) electron statistics and on the dust concentration has been investigated. • A damped Korteweg-de Vries equation is derived for electrostatic solitary waves. • Solitary wave polarity (sign) is reversed when dust concentration exceeds a threshold. • Landau damping and dust effects weaken and slow down the solitary wave over time. • Dispersive effects may be dominant, leading to oscillatory shock profiles. • Lower κ values favor monotonic shock structures against oscillatory profiles.