Exploring the physical characteristics and nonlinear wave dynamics of a (3+1)-dimensional integrable evolution system.

This study comprehensively explores the (3 + 1) -dimensional Mikhailov–Novikov–Wang (ℕ) integrable equation, with the primary objective of elucidating its physical manifestations and establishing connections with analogous nonlinear evolution equations. The investigated model holds significant physical meaning across various disciplines within mathematical physics. Primarily, it serves as a fundamental model for understanding nonlinear wave propagation phenomena, offering insights into wave behaviors in complex media. Moreover, its relevance extends to nonlinear optics, where it governs the dynamics of optical pulses and solitons crucial for optical communication and signal processing technologies. Employing analytical methodologies, namely the unified () , Khater II ( hat.II) method, and He's variational iteration (ℍ ) method, both numerical and analytical solutions are meticulously examined. Through this investigation, the intricate behaviors of the equation are systematically unveiled, shedding illuminating insights on various physical phenomena, notably including wave propagation in complex media and nonlinear optics. The outcomes not only underscore the efficacy of the analytical techniques deployed but also accentuate the equation's pivotal role in modeling a broad spectrum of nonlinear wave dynamics. Consequently, this research significantly advances our comprehension of complex physical systems governed by nonlinear dynamics, thereby contributing notably to interdisciplinary pursuits in mathematical physics. [ABSTRACT FROM AUTHOR]