Bilinearization and new center-controlled N-rogue solutions to a (3+1)-dimensional generalized KdV-type equation in plasmas via direct symbolic approach

This research studies rogue wave solutions with center parameters of a generalized (3+1)-dimensional KdV-type equation in plasma physics. Using a direct generalized formula and symbolic technique, it creates rogue waves with adjustable dynamical characteristics controlled by the center parameters. Our investigation produces rogue wave solutions up to the third order with Painlevé transformation through direct computation, considering a range of center-controlled and other parameters within the investigated equation. To facilitate our analysis, we derive an equation for the function f in bilinear form, utilize the Cole-Hopf transformation for the wave function u, and introduce the transformed variable \(\zeta \) $\zeta$ . It obtains the rogue wave solutions using a generalized form for N-rogue waves generated from Hirota’s N-soliton approach. Through the powerful symbolic computation tool Mathematica, we provide visualizations of the dynamic behavior of rogue waves across diverse center parameters. This 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 longer waves characterized by smaller amplitudes, which is particularly relevant in plasma physics, fluid dynamics, and dispersive media. Rogue waves have applications in diverse scientific fields, including oceanography, nonlinear dynamics, fluid dynamics, fiber optics, dusty plasma, and complex nonlinear systems