# Envelope solitons in double pair plasmas

## TL;DR

This paper derives a nonlinear Schrödinger equation for double pair plasmas with super-thermal electrons and positrons, revealing how super-thermality influences envelope soliton formation and stability in space and lab plasmas.

## Contribution

It introduces a model for ion-acoustic wave modulation in double pair plasmas with super-thermal particles, highlighting the impact of super-thermality on soliton dynamics and stability.

## Key findings

- Dark and bright envelope solitons form depending on stability conditions.
- Super-thermality enhances nonlinearity and accelerates bright soliton formation.
- Presence of super-thermal particles modifies the modulational stability regions.

## Abstract

A double pair plasma system containing cold inertial positive and negative ions, and inertialess super-thermal electrons and positrons is considered. The standard nonlinear Schr\"{o}dinger equation is derived by using the reductive perturbation method to investigate the nonlinear dynamics of the ion-acoustic waves (IAWs) as well as their modulation instability. It is observed that the ion-acoustic dark (bright) envelope solitons are formed for modulationally stable (unstable) plasma region, and that the presence of highly dense super-thermal electrons and positrons enhances (reduces) this unstable (stable) region. It is also found that the effect of super-thermality of electron or positron species causes to increase the nonlinearity, and to fasten the formation of the bright envelope solitons. These results are applicable to both space and laboratory plasma systems for understanding the propagation of localized electrostatic disturbances.