Modulational instability of dust-ion-acoustic waves and associated first and second-order rogue waves in super-thermal plasma

TL;DR

This paper investigates the modulational instability of dust-ion-acoustic waves in a super-thermal plasma, deriving a nonlinear Schrödinger equation to analyze rogue wave formation influenced by plasma parameters in astrophysical and laboratory settings.

Contribution

It introduces a novel nonlinear Schrödinger equation for dust-ion-acoustic waves in super-thermal plasma, analyzing MI conditions and rogue wave structures considering multiple plasma parameters.

Findings

MI conditions depend on plasma charge, mass, temperature, and density.

Two types of DIA modes: fast and slow.

Rogue waves are formed in the unstable regime influenced by plasma parameters.

Abstract

A proper theoretical research has been carried out to explore the modulational instability (MI) conditions of dust-ion-acoustic (DIA) waves (DIAWs) in a three-component dusty plasma system containing inertialess $\kappa$-distributed electrons, and inertial warm positive ions and negative dust grains. The novel nonlinear Schr\"{o}dinger equation (NLSE) has been derived by employing the reductive perturbation method. The analysis under consideration demonstrates two types of modes, namely, fast and slow DIA modes. The dispersion and nonlinear properties of the plasma medium, as well as the MI conditions of DIAWs and the configuration of the energetic rogue waves (RWs) associated with DIAWs in the Modulationally unstable regime, have been rigorously changed by the plasma parameters, namely, charge, mass, temperature, and number density of the plasma species. The findings of our investigation will be useful in understanding the criteria for the formation of electrostatic RWs in both astrophysical environments (viz., Jupiter's magnetosphere, cometary tails, Earth's mesosphere, Saturn's rings, etc.) and laboratory experiments (viz., Q-machines and Coulomb-crystal).