Quantum Dust Acoustic Wave Dynamics in Nonuniform Dusty Plasma via a Dual-Mode Modified KdV Equation

The behavior of nonlinear quantum dust acoustic (NLQDA) waves in a quantum dusty plasma (QDP) is investigated using a hydrodynamical quantum plasma model. The reductive perturbation methodology is employed to demonstrate that the fundamental equations for the hydrodynamical quantum model, illustrating NLQDA waves, yield a dual-mode modified Korteweg-de Vries (mKdV) equation. To develop the hydrodynamical quantum model for plasmas, the dual-mode modified Korteweg-de Vries equation is derived using the Sardar sub-equation method. Through this investigation, novel and inclusive solutions for NLQDA waves are unearthed, expressed through a rich tapestry of generalized hyperbolic and trigonometric functions. The solutions obtained through the computational analysis are subjected to rigorous validation procedures, employing the powerful computational tools provided by Maple software. Through this comprehensive verification process, the accuracy and reliability of the findings are ensured, and the credibility of the research outcomes is enhanced. The solutions obtained are visually represented through various graphical techniques, including two-dimensional (2D), three-dimensional (3D), and contour plots, and the physical characteristics and behavior of the acquired solutions are elucidated. The effectiveness of the proposed approach in discerning the characteristics of NLQDA waves in QDP is demonstrated by the outcomes.