On the exploration of soliton solutions of the nonlinear Manakov system and its sensitivity analysis

In this study, we investigate the fractional coupled nonlinear Schrödinger equation (FCNLSE) of Manakov type, which has numerous applications in different fields of physics, such as optics and plasma physics. In this study, we employ two different analytical methods, namely the auxiliary equation method (AEM) and the improved F-expansion method, to construct novel analytic exact solitary wave solutions, encompassing trigonometric, hyperbolic, and exponential functions. These solutions include solitary wave solutions dark, bright, combo, singular, rational form solutions, and periodic wave solutions. Additionally, using the characterizations of the Hamiltonian system, the stability property of the discovered soliton wave solutions is examined. We have also illustrated the sensitivity analysis for the modified dynamic structural system using different initial conditions. In order to illustrate various physical properties of wave structures, the well-furnished results are finally demonstrated in various 3D, 2D, contour, and density profiles. This work’s findings highlight the significance of researching diverse nonlinear wave phenomena in physics and nonlinear optics by demonstrating how crucial it is to comprehend the physical meaning and behavior of the examined equation. The procedures used are capable, effective, and succinct enough to make it possible for further research