Investigating higher dimensional Jimbo–Miwa nonlinear dynamics through phase portraits, sensitivity, chaos and soliton behavior

Abstract

The main focus of this article is on the development of new wave structures for the nonlinear (3+1)-dimensional Jimbo–Miwa equation. To solve the Jimbo–Miwa equation, a modified Khater method has been employed to generate various forms of soliton wave structures. Exact solutions to this equation are considered important for the complete understanding of the dynamics of waves in a physical model. The dynamic behavior of wave structures, including solutions for brilliant, single, dark, and periodic singular solitons, is enlightened by the obtained results. Selected solutions are plotted in both two- and three-dimensional graphs to illustrate their behavior. Furthermore, the system is converted into a planar dynamical system, and the derived solutions are examined using phase portraits to illustrate and demonstrate the theoretical results. Bifurcation and chaos theories are applied to enhance comprehension of the planar dynamical system that emerges from the examined system. Additionally, an investigation into the sensitivity of the provided model is conducted, revealing a moderate level of sensitivity and stability. These innovative concepts are utilized through symbolic computations to provide comprehensive and powerful mathematical tools for addressing various benign nonlinear problems.