Bifurcation, chaos, and time series analysis of the Manakov model utilizing the unified Riccati equation expansion technique

The Manakov model is an extended version of the Schrödinger problem that appears in various domains of optical system and radiation particles. This research focuses on analyzing the bifurcation, chaos, and time series of the Manakov model. This study involves two distinct phases. The unified Riccati equation expansion technique (UREET) is employed to construct distinct optical solutions which includes the solutions of dark, solitary, periodic, and planar wave. Furthermore, we explore the dynamic characteristics of chaos, bifurcation, and time series analysis of the governing model through the use of the Galilean transformation. The bifurcation findings provide a geometrical perspective on the dynamic characteristics of the Manakov model. We offer an extensive behavior of these dynamic systems by showcasing various outcomes through contour, phase plane, 2D, and 3D graphs. Our results indicate the significance of the various nonlinear wave behaviors in nonlinear optical models of physical sciences.