Three-dimensional modulational instability of dust acoustic waves in the presence of generalized (r, q) distributed electrons

Abstract

A three-dimensional (3D) modulational instability (MI) of dust acoustic waves (DAWs) in a three-component magnetized dusty plasma system consisting of a negatively charged fluid, inertialess generalized (r, q) distributed electrons and Boltzmann distributed ions, is investigated. The basic system of the nonlinear hydrodynamic equations is reduced to a 3D nonlinear Schrödinger equation (NLS) which is valid for small but finite amplitude DAWs using a reductive perturbation technique. The domain of the stability and instability regions is investigated that is strongly affected by the spectral parameters of the generalized (r, q) distribution and the electron-to-ion temperature ratio (T e /T i ). The existence domains for observing the first-and second-order solutions of the dust acoustic rogue waves (DARWs) are determined and the basic features (viz the width and amplitude) for the first-order solution are found to be significantly dependent on the system physical parameters changes such as T e /T i , number density ratio [n e0/(n d0 z d0)] and the dust cyclotron frequency (ω cd ) as well as the spectral indexes r and q. A comparison between the first-and second-order DARW amplitudes is presented. Moreover, another comparison between the first-order DARW amplitudes obtained by generalized (r, q) distributed electrons and those corresponds to Maxwellian is provided. Finally, implication of our consequences in specific plasma situations are briefly discussed.