Complex Korteweg-de Vries equation and Nonlinear dust-acoustic waves in a magnetoplasma with a pair of trapped ions

TL;DR

This paper derives a complex KdV-like equation describing small-amplitude dust-acoustic waves in a magnetized dusty plasma with trapped ions, revealing effects of magnetic fields, dust pressure, and ion properties.

Contribution

It introduces a novel complex KdV equation for dust-acoustic waves in magnetized plasmas with trapped ions, incorporating vortex-like ion distributions.

Findings

Complex coefficient due to ion distributions affects wave evolution.

Magnetic field influences wave amplitude and speed.

Dust pressure and ion properties significantly modify wave behavior.

Abstract

The nonlinear propagation of dust-acoustic (DA) waves in a magnetized dusty plasma with a pair of trapped ions is investigated. Starting from a set of hydrodynamic equations for massive dust fluids as well as kinetic Vlasov equations for ions, and applying the reductive perturbation technique, a Korteweg-de Vries (KdV)-like equation with a complex coefficient of nonlinearity is derived, which governs the evolution of small-amplitude DA waves in plasmas. The complex coefficient arises due to vortex-like distributions of both positive and negative ions. An analytical as well as numerical solution of the KdV equation are obtained and analyzed with the effects of external magnetic field, the dust pressure as well as different mass and temperatures of positive and negative ions.