Investigation of Modulational Instability Drift Wave Packet in Non-uniform Magneto-Rotating Plasma

This paper addresses the modulation instability of ion-acoustic waves in a rotating plasma subjected to a magnetic field, focusing on how inhomogeneities in equilibrium density, electron temperature, and magnetic field influence wave behavior. We employ a combined hydrodynamic approach and perturbation method to derive the nonlinear Schrödinger equation (NLSE), effectively balancing nonlinearity with dispersive effects. Our analysis reveals various localized ion-acoustic excitations, including bright and dark envelope solitons, which emerge from modulational instability. We also demonstrate that specific solutions of the NLSE, such as the Peregrine soliton, Akhmediev breather, and Kuznetsov-Ma breather, represent rogue wave phenomena within this context. Numerical simulations indicate that plasma structural parameters, including rotational frequency and scale lengths, significantly impact modulation instability conditions. Notably, while these parameters enhance instability, further increases can lead to a reduction in rogue wave amplitude. Our findings provide insights into the formation mechanisms of nonlinear electrostatic excitations in both ultra-dense astrophysical and experimental plasma environments.