Analysis of the dynamical perspective of chaos, Lie symmetry, and soliton solution to the Sharma–Tasso–Olver system

This current work examines the 2-dimensional Sharma–Tasso–Olver system ( STOS ). This system is crucial for precise wave motion in real-world applications such as wireless networks, systems for control, and digital signal processing. There are three major goals for this investigation. Firstly, the Lie symmetries are constructed and the corresponding transformation is used to reduce the model to an ordinary differential equation. Invariant solutions are established and illustrated via plots. Secondly, we employ the unified Riccati equation expansion ( UREE ) approach to obtain several unique soliton solutions, including single, dark periodic, and rational wave solutions across several physical domains for the STOS . Thirdly, we explore the chaotic structure with and without perturbation to the governing model with time series analysis by using chaos theory. The investigations, which concentrate on the nonlinear dynamic behaviors of the solutions, are new and unexplored. These behaviors are shown in 3-D plots, contour plots, 2-D curves, and descriptions of the related physical properties. Our findings demonstrate that the UREE approach can potentially be used for producing soliton solutions and analyzing them in nonlinear models and dynamic data. This method offers useful mathematical tools and can be applied to the study of wave motion in a dispersive medium.