# Dust-acoustic envelope solitons in super-thermal plasmas

## TL;DR

This paper investigates how super-thermal particles influence the stability of dust-acoustic waves in a complex plasma, revealing how their presence alters the conditions for modulational instability through nonlinear analysis.

## Contribution

It introduces a detailed analysis of dust-acoustic wave stability in super-thermal plasmas using the nonlinear Schrödinger equation and identifies how super-thermal particles modify stability regions.

## Key findings

- Super-thermal particles significantly alter stable and unstable wave regions.
- The critical wave number for instability depends on particle concentrations.
- Two distinct parametric regions for wave stability are identified.

## Abstract

The modulational instability (MI) of the dust-acoustic waves (DAWs) in an electron-positron-ion-dust plasma (containing super-thermal electrons, positrons and ions along with negatively charged adiabatic dust grains) is investigated by the analysis of the nonlinear Schr\"{o}dinger equation (NLSE). To derive the NLSE, the reductive perturbation method has been employed. Two different parametric regions for stable and unstable DAWs are observed. The presence of super-thermal electrons, positrons and ions significantly modifies both the stable and unstable regions. The critical wave number $k_c$ (at which modulational instability sets in) depends on the super-thermal electron, positron, and ion, and adiabatic dust concentrations.