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

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 Schrodinger 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 (omega(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.

Automated summary

The three-dimensional modulational instability of dust acoustic waves in a three-component magnetized dusty plasma system is investigated, showing that the first and second-order solutions of dust acoustic rogue waves have different features dependent on various physical parameters. Comparisons between different amplitudes and solutions obtained from different electron distributions are made, and implications in specific plasma situations are briefly discussed.