Modulational instability and associated low-frequency dust-acoustic waves in a degenerate Thomas-Fermi plasma: Envelope solitons and rogue waves

Abstract

This paper examines the modulational instability (MI) of low-frequency dust-acoustic waves in a dusty quantum plasma that contains inertial dust particles and inertialess Thomas-Fermi distributed ions and electrons. In this model, the ions and electrons are assumed to be in a degenerate quantum state. By using a reductive perturbation technique, the fluid governing equations are reduced to an evolutionary equation (say, a nonlinear Schrödinger equation that governs this phenomenon). A detailed investigation is carried out on the dispersion relation, group dispersion coefficient, nonlinearity coefficient, and the regions of the MI. Regions of stability and instability are precisely determined based on the MI criteria and the pertinent physical parameters of the model under examination. We also examine some nonlinear modulated phenomena (localized envelope structures), such as dark, bright envelope solitons, rogue waves, and breathers that can propagate in stable and unstable regions.