ABSTRACT The present study explores the three‐dimensional wave group dynamics and breather excitations associated with dust‐acoustic waves (DAWs) in a superthermal magnetized dusty plasma system. The plasma is assumed to consist of inertialess electrons and ions obeying a kappa distribution, and a negatively charged inertial dust fluid under the influence of an external uniform magnetic field. By employing the reductive perturbation method, we derive the Laedke‐Spatschek (LS) equation, which governs the dynamics of the nonlinear DAWs in such a plasma configuration. Analytical solutions of the evolution equation predict a wide class of nonlinear localized structures. Furthermore, the analysis reveals that the modulated wave group dynamics can be effectively described by a ‐dimensional nonlinear Schrödinger equation (NLSE), accounting for both nonlinear and dispersive effects. The regions of stability and instability of the DAW propagation are delineated in the relevant plasma parameter space, identifying the conditions under which rational breather solutions of NLSE, such as the Peregrine soliton, Akhmediev breather, and Kuznetsov‐Ma breather can be excited through modulational instability. The findings provide a comprehensive understanding of the proliferation of nonlinear wave modulation and energy localization phenomena in dusty plasma environments, with potential implications for both space and laboratory plasma systems.
Ghosh et al. (Mon,) studied this question.