Dynamics behavior of solitons based on exact solutions for the mathematical model arising in telecommunications

In this paper, the Jimbo–Miwa equation (JME) is a prominent integrable nonlinear partial differential equation within the Kadomtsev–Petviashvili (KP) hierarchy, widely studied for its applications in soliton theory and mathematical physics. This work explores the extension of the standard (2+1)-dimensional JME to a (3+1)-dimensional form, incorporating an additional spatial dimension to model more complex physical phenomena. The extended (3+1)-dimensional JME retains the integrability properties of the original equation, admitting exact solutions such as solitons and multi-soliton solutions. Analytical methods such as the sine-Gordon expansion method and the traveling wave are employed to construct exact solutions. This study highlights the significance of the (3+1)-dimensional JME in advancing our understanding of nonlinear dynamics in higher-dimensional systems, with potential applications in fluid dynamics, plasma physics, and other fields.