Modulational instability of dust-ion-acoustic mode and associated rogue waves in a non-extensive plasma medium

TL;DR

This paper investigates the modulational instability and rogue wave formation of dust-ion-acoustic modes in a non-extensive dusty plasma, revealing how plasma parameters influence stability and wave characteristics.

Contribution

It derives a nonlinear Schrödinger equation for the system and analyzes how plasma parameters affect modulational instability and rogue wave formation, including effects of non-extensive statistics.

Findings

Modulational stability depends on plasma parameters and non-extensive q.

Rogue wave amplitude and width are influenced by ion mass and dust charge.

Stability regimes are significantly modified by non-extensive parameter q.

Abstract

The modulational instability of dust-ion-acoustic (DIA) mode and associated rogue waves in a three component dusty plasma system (containing inertial warm ion and negatively charged dust fluids along with inertialess $q$-distributed electrons) has been theoretically investigated. A nonlinear Schr\"{o}dinger equation (NLSE) has been derived by employing the reductive perturbation method. It is observed that the dusty plasma system under consideration supports the fast and slow DIA modes, and that the dispersion and nonlinear coefficients of the NLSE determine the parametric regimes not only for the modulationally stable and unstable fast DIA mode, but also for the formation of the DIA rogue waves. The parametric regimes for the modulational instability of the fast DIA mode, and the criterion for the formation of the DIA rogue waves have been found to be significantly modified by the effects of the relevant plasma parameters, particularly, mass and charge state of ion and dust species, number density of the plasma species, and non-extensive parameter $q$, etc. It is found that the modulationally stable parametric regime decreases (increases) with the increase in the value of positive (negative) $q$. The numerical analysis has also shown that the nonlinearity as well as the amplitude and width of the rogue waves increases (decreases) with the mass of positive ion (negative dust grains) while decreases (increases) with the charge state of the positive ion (negative dust). The applications of our present work in space (viz., Earth ionosphere, magnetosphere, molecular clouds, interstellar medium, cometary tails, and planetary rings, etc.) and laboratory plasmas have been pinpointed.