Exploring the dynamic nature of soliton solutions to the fractional coupled nonlinear Schrödinger model with their sensitivity analysis

This study investigates the fractionally coupled nonlinear Schrödinger model (FCNLSM), which has numerous applications in different fields of physics, such as optics, condensed matter physics and plasma physics. The study employs two versatile techniques, the unified technique and the modified ℱ -expansion technique, to explore various solutions. By applying these techniques, we obtain novel soliton solutions, which are expressed in terms of rational, hyperbolic and trigonometric solutions, along with kink, periodic and singular soliton solutions. Additionally, multi-wave U-shaped solitary wave solutions are assessed. The sensitivity analysis of the model is investigated and distinctive 2-dimensional, 3-dimensional and density graphs are used to illustrate the behavioral characteristics of the retrieved solutions. As far as we know, this manner of investigation has never been explored before. The results demonstrate the reliability, consistency and effectiveness in finding precise solutions to the various difficult nonlinear issues that arise in engineering, applied sciences and nonlinear optics.