Integrating data overlaps and nonlinear dynamics: A novel approach to the Davey-Stewartson system in optical fluid model

Abstract

In this study, the newly developed (2 + 1)-dimensional Davey-Stewartson system, characterized by parabolic law nonlinearity, is examined. This equation is recognized as significant for modeling surface wave patterns in finite-depth conditions. The model is initially transformed into lower dimensions using the wave transformation. Various soliton solutions, including kink, anti-kink, periodic, and chirped solitons, are derived using the generalized logistic equation method. These soliton structures have practical applications in fields such as optical pulse propagation in fiber optics, signal transmission in communication systems, energy transport in ocean engineering, and biological wave modeling, particularly in understanding nonlinear wave dynamics in shallow water and geophysical flows. To deepen our understanding of the physics behind these solutions, they are visualized using various representations, including 3D plots, 2D plots, density plots, and polar plots. Following this, a phase portrait analysis is conducted on the critical points of the unperturbed dynamical system. Subsequently, an outward force is introduced, and the perturbed system's behavior is examined using advanced chaos detection techniques. These include Poincaré maps, time series graphs, multistability analysis, chaotic attractors, return maps, power spectra, and Lyapunov exponents. A newly introduced bidirectional scatter plot approach is employed to perform a comparative analysis of solution behaviors, effectively highlighting overlapping regions and distinctions within their solution spaces through data points. This study contributes to the understanding of nonlinear wave systems and provides new tools for future research in applied mathematics.