Dynamical investigation of the nonlinear Schrödinger equation with second-order spatiotemporal involvement of the time-conformable operator

The article analyzes the application of the extended hyperbolic function technique to a conformable-operator nonlinear Schrödinger equation, incorporating group velocity dispersion coefficients and second-order spatiotemporal components. The primary objective is establishing a spectrum of solutions directly pertinent to optical fibers. The extracted results, which include bright, singular, straddled, dark-bright, and dark solitons, are obtained by hyperbolic and trigonometric function-type solutions. We exhibit contour plots with two-dimensional and three-dimensional visualizations to emphasize the implication of the proposed conformable-operator nonlinear Schrödinger equation and to depict the diverse novel optical solutions. Additionally, we study the impact of the conformable operator on these solutions, employing graphical analysis to demonstrate its implications. The governing model shows potential applications in transmitting ultra-fast pulses via optical fibers.