Bifurcation analysis, chaotic behavior, sensitivity demonstration and dynamics of fractional solitary waves to nonlinear dynamical system

In various fields of nonlinear sciences, fractional derivatives improve the accuracy and understanding of nonlinear dynamics. This study explores the fractional (2+1) dimensional nonlinear Schrödinger equation arising in the diversity of engineering fields. A variety of solitary wave solutions have been discussed with the assistance of advanced integration methods, namely the modified generalized Riccati equation mapping approach and F-expansion technique. The obtained solutions are displayed in graphs of relevant parameter values to elucidate the physical meaning and scientific interpretation of the analytical work. This paper's main contribution is an examination of the qualitative study like sensitivity analysis, chaotic behavior, and bifurcation analysis. The Galilean transformation is used for the qualitative analysis. Additionally, the behavior of time-varying dynamical systems is investigated through the perspective of chaos theory. To uncover the evasive character of chaos, we investigate 3D, 2D, phase portraits, time series, and Poincare mapping as potent instruments.