Modulational instability and dynamics of multidimensional dust ion-acoustic wave envelope in collisional dense astrophysical dusty plasma

We study the nonlinear propagation of (2+1)-dimensional modulated dust ion-acoustic waves (DIAW’s) envelope considering a semiclassical, two-fluid hydrodynamic model incorporating the effects of electron exchange–correlation potential, quantum Bohm potential term and degenerate pressure in unmagnetized collisional dusty plasma. We employ standard multiple-scale perturbation technique to obtain a (2+1)-dimensional modified nonlinear Schrödinger (mNLS) equation describing the slow modulation of DIAW packets’ evolution. It is noticed that the NLS equation is modified with a damping term due to the presence of dust-neutral collisional effects, which significantly alter the behavior of the system. Also, we investigate the oblique modulational instability (MI) by means of the corresponding mNLS equation. Various instability criteria and instability domains are identified exclusively, and the corresponding growth rate of MI is obtained in the unstable domain. Moreover, analytic solutions (such as breather solutions) of the mNLS equation are obtained using Hirota’s method. In the current framework, MI enhances coherence within nonlinear plasma systems by reducing wave randomness and mitigating random phase fluctuations. This process enables the formation of coherent, self-organized structures such as DIA envelope solitons or wave collapse. These variations may result in rogue waves, which are unexpected localized wave formations within the turbulent plasma environment. We also perform parametric analysis and observe that the key plasma parameters, viz., electron exchange–correlation potential, ion and electron number densities, remarkably change the criteria and domains of MI, as well as the characteristics features of DIAW’s propagation (via the rough and breather structures). The relevance of this present theoretical investigation is pointed out in dense astrophysical objects like the interior of white dwarf stars for exploring the nonlinear dynamics of DIAW.