Analysis of bifurcation and optical solitons in fiber Bragg gratings with conformable beta-derivative

In this study, we amalgamate the optical soliton solutions to the dimensionless form of the fractional coupled nonlinear Schrödinger equation (FCNLSE) in fiber Bragg gratings (FBGs) with dispersive reflectivity along with Kerr law of nonlinear refractive index. FBGs is a technological spectacle that exhibit the nonlinear effects due to the Kerr nonlinearity, where the refractive index of the fiber core varies with the intensity of the light passing across it. With the use of the newly created computational technique, the new extended direct algebraic method (NEDAM), we were able to manifest the novel optical soliton solutions, which have not been previously documented in the literature, in the framework of hyperbolic soliton, periodic, periodic-singular, multi-dark, dark-bright, bright-dark, mixed trigonometric, singular as well as rational. Moreover, validation of the solutions is carried out utilizing the Hamiltonian property, confirming the accuracy and stability of segregated optical solitary wave solutions. We also conduct a thorough bifurcation analysis to look into the bifurcation events that the FCNLSE displays. We also perform sensitivity analysis to investigate the robustness of the chosen model against changes in initial conditions and parameters, which offers an understanding of the system’s susceptibility to disturbances. We provide 3-D and 2-D visualisations of optical soliton wave solutions and phase plane analysis using Mathematica 11.0 and Matlab’s rk4 and ode45 algorithms. Using numerical simulations and analytical tools, we show how effective our proposed technique is in analyzing the FCNLSE, providing new insights into their behavior and solutions. Our results offer fresh perspectives on the dynamics of FCNLSE and contribute to the development of mathematical instruments for studying nonlinear partial differential equations, which have many characteristics in the area of applied mathematics and physics.