On nonlinear wave structures, stability analysis and modulation instability of the time fractional perturbed dynamical model in ultrafast fibers

The nonlinear Schrödinger equation (NLSE) is the most significant physical model to explain the fluctuations of optical soliton proliferation in optical fiber theory. Optical soliton propagation in nonlinear fibers is currently a subject of great interest due to the multiple prospects for ultrafast signal routing systems and short light pulses in communications. In this article, the time-fractional perturbed NLSE that demonstrates the super fast wave propagation in optical fibers is investigated analytically. To better understand the underlying mechanisms for these kinds of nonlinear systems, the results are displayed using 3D, 2D, and contour graphics. Furthermore, it is confirmed that the established results are stable, and the modulation instability for the governing model is also studied. The computational intricacies and results highlight the clarity, efficacy, and simplicity of the approaches, pointing to the applicability of these methods to various sets of dynamic and static nonlinear equations governing evolutionary phenomena in computational physics, as well as to other practical domains and a variety of research fields.