Investigating the Dynamics of a Unidirectional Wave Model: Soliton Solutions, Bifurcation, and Chaos Analysis

Abstract

The current work investigates a recently introduced unidirectional wave model, applicable in science and engineering to understand complex systems and phenomena. This investigation has two primary aims. First, it employs a novel modified Sardar sub-equation method, not yet explored in the literature, to derive new solutions for the governing model. Second, it analyzes the complex dynamical structure of the governing model using bifurcation, chaos, and sensitivity analyses. To provide a more accurate depiction of the underlying dynamics, they use quantum mechanics to explain the intricate behavior of the system. To illustrate the physical behavior of the obtained solutions, 2D and 3D plots, along with a phase plane analysis, are presented using appropriate parameter values. These results validate the effectiveness of the employed method, providing thorough and consistent solutions with significant computational efficiency. The investigated soliton solutions will be valuable in understanding complex physical structures in various scientific fields, including ferromagnetic dynamics, nonlinear optics, soliton wave theory, and fiber optics. This approach proves highly effective in handling the complexities inherent in engineering and mathematical problems, especially those involving fractional-order systems.