BRIJ MOHAN

This conference abstract presents a research study of a novel (3+1)-dimensional nonlinear partial differential equation. This research investigates the complete integrability of this equation through the standard Painlev\'e test. Using a direct generalized formula and symbolic computation techniques, we create rogue waves with adjustable dynamical characteristics controlled by the center parameters. Our investigation produces rogue wave solutions up to third-order through direct computation, considering a range of center-controlled parameter values and selecting appropriate constants within the equation. To facilitate our analysis, we derive a bilinear equation in the auxiliary function $f$, utilize the Cole-Hopf transformation for the dependent variable $u$, and introduce the transformed variable $\zeta$. Applying the direct approach of $N$-soliton solutions in Hirota's direct method to generate rogue waves up to the third order, we employ a generalized formula based on $N$-soliton solutions. Through the powerful symbolic computation tool \textit{Mathematica}, we provide visualizations of the dynamic behavior of rogue waves across diverse center-controlled parameters. Furthermore, our research highlights the prevalence of massive rogue waves within nonlinear phenomena, showcasing their dominance over their smaller counterparts. The investigated equation offers insights into the evolution of long waves characterized by small amplitudes, particularly relevant in plasma physics, wave motion in fluids, and weakly dispersive media. Rogue waves find applications in diverse scientific fields, including oceanography, fluid dynamics, dusty plasma, optical fibers, and nonlinear dynamics, in understanding complex nonlinear systems.