Nonlinear Dynamics of Dust Acoustic Waves in a Dusty Plasma in Presence of Two Opposite Polarity Dust Species

In a non-linear dynamical structure, this research presents a new analytical framework for examining the Zakharov-Kuznetsov equation in the realm of dusty ion-acoustic waves. Our objective is to produce a wide range of optical solitons at a reduced cost and time scale for evaluation by employing specific integration techniques. To achieve this, we are using two analytical approaches: the unified Ricatti equation procedure and the new extended auxiliary equation strategy. These methods help us to discover a variety of exact solutions for the governing model, including solitary, rational, elliptic functions, and periodic waves. Using numerical simulations and graphical representations, we further examine the features and properties of these solutions. The approach’s significance is described by comparing it with mathematical simulations and current analytical solutions, which emphasize its precision and adaptability in portraying the intricate nature of ion-acoustic waves. The obtained results reflect that the suggested framework displays a wide range of diverse and rich wave phenomena and also demonstrate that the proposed techniques for resolving non-linear partial differential equations that arise in the field of mathematical physics are efficient, helpful, and reliable for future discoveries.