Exploring the Depths: Soliton Solutions, Chaotic Analysis, and Sensitivity Analysis in Nonlinear Optical Fibers

Abstract

This paper discusses the time-fractional nonlinear Schrödinger model with optical soliton solutions. We employ the f+(G′G)-expansion method to attain the optical solution solutions. An important tool for explaining the particular explosion of brief pulses in optical fibers is the nonlinear Schrödinger model. It can also be utilized in a telecommunications system. The suggested method yields trigonometric solutions such as dark, bright, kink, and anti-kink-type optical soliton solutions. Mathematica 11 software creates 2D and 3D graphs for many physically important parameters. The computational method is effective and generally appropriate for solving analytical problems related to complicated nonlinear issues that have emerged in the recent history of nonlinear optics and mathematical physics. Furthermore, we venture into uncharted territory by subjecting our model to chaotic and sensitivity analysis, shedding light on its robustness and responsiveness to perturbations. The proposed technique is being applied to this model for the first time.