Bifurcation Analysis and Soliton Structures of Davey-Stewartson Fokas System

In this research, we studied the (2+1)-dimensional Davey-Stewartson Fokas (DS-Fokas) system, which serves as an optimal model for nonlinear pulse propagation in mono-mode optical fibers. We employ the Jacobi elliptic function approach to obtain the novel soliton solutions for the DS-Fokas system. The employed method is a very efficient and robust mathematical approach for solving non-linear models of various nonlinear Schrödinger’s equations (NLSEs) in mathematical physics and sciences. The obtained solutions are useful and significant in elucidating the DS-Fokas system's physical aspects, as they provide insights. Furthermore, we discuss these obtained solutions graphically using 3D and 2D graphs to gain a deep understanding and vision of the analytical results. We also looked at the unpredictable and changing behaviors of the system we studied by using phase portraits, quasi-periodic and chaotic portraits, Poincare maps, bifurcation diagrams, and sensitivity. The theory of planar dynamical systems looks at chaotic patterns in the systems under study when the disturbance term $\cos \omega t$ is added. Numerical simulations demonstrate how changes in frequency and amplitude impact the dynamics of the system.