Modulational Instability of Dust-Ion-Acoustic Modulated Envelope Structures in Ultracold Quantum Complex Plasmas: Solitons, Rogue Waves, and Breathers

Abstract

In this study, we use a one-dimensional quantum hydrodynamic model to investigate the dynamics of amplitude-modulated dust ion-acoustic waves (DIAWs) in an ultracold, three-component quantum complex plasma composed of inertialess electrons, inertial ions, and immobile negatively charged dust particles. A nonlinear Schrödinger equation (NLSE) is reduced from the set of fluid equations via the reductive perturbation technique. The dispersion relation and group velocity are found to depend upon the wave number and related plasma parameters (i.e., the quantum diffraction parameter and dust concentration). It is noted that dispersion and nonlinear coefficients vary with wave number and parametric values of plasma. We thoroughly examined the modulational instability (MI) calculated from the NLSE, finding that dust concentration and the diffraction parameter significantly influence the conditions for the MI. Based on the MI criteria and relevant physical plasma parameters, the regions of stability and instability are carefully identified. Furthermore, we explored nonlinear modulated structures such as bright-type envelopes (pulses), dark-type envelope solitons (holes or voids), breathers, and rogue waves, which can propagate in both stable and unstable regions.