Electromagnetic effects on solitons propagation of the (3+1)-dimensional extended Zakharov–Kuznetsov dynamical model with applications

This paper investigates wave solutions and electromagnetic wave phenomena governed by the (3+1)-dimensional extended Zakharov–Kuznetsov equation (EZKE) utilizing the Sardar sub-equation method. With a focus on electromagnetic wave generation and propagation, we rigorously analyze fundamental properties, soliton solutions, and dynamic behaviors of the EZKE. Through this analytical technique, we unravel the complex interplay among various wave types, including solitary waves and electromagnetic structures, elucidating their formation mechanisms and interaction dynamics. Furthermore, we delve into the stability characteristics of the EZKE, enhancing our understanding of its mathematical and physical implications. Our findings not only contribute to theoretical insights into nonlinear wave phenomena in (3+1)-dimensional space but also hold practical significance in plasma physics, nonlinear optics, and electromagnetic wave propagation. This study advances the development of innovative wave manipulation and control techniques, with applications ranging from plasma confinement in fusion devices to the design of advanced photonic devices for telecommunications and sensing purposes.