Nonlinear dust-acoustic solitary waves and shocks in dusty plasmas with a pair of trapped ions

TL;DR

This paper investigates the formation and properties of dust-acoustic solitary waves and shocks in dusty plasmas containing trapped positive and negative ions, using reductive perturbation techniques to derive complex KdV and Burgers' equations.

Contribution

It introduces a novel analysis of dust-acoustic waves considering trapped ions and dust charge variations, deriving evolution equations for solitary waves and shocks.

Findings

Dust charge variation significantly affects wave profiles.

Trapped ions influence the amplitude and width of solitary waves.

The derived equations describe complex wave behaviors in dusty plasmas.

Abstract

The propagation characteristics of small-amplitude dust-acoustic (DA) solitary waves (SWs) and shocks are studied in an unmagnetized dusty plasma with a pair of trapped positive and negative ions. Using the standard reductive perturbation technique with two different scaling of stretched coordinates, the evolution equations for DA SWs and shocks are derived in the forms of complex Korteweg-de Vries (KdV) and complex Burgers' equations. The effects of dust charge variation, the dust thermal pressure, and the ratios of positive to negative ion number densities as well as the free to trapped ion temperatures on the profiles of SWs and shocks are analysed and discussed.