Analysis of optical solutions of higher-order nonlinear Schrödinger equation by the new Kudryashov and Bernoulli’s equation approaches

The optical soliton solutions of the time-fractional higher-order nonlinear Schrödinger equation in the presence of the Kudryashov nonlinear refractive index are studied in this paper using the new Kudryashov approach and Bernoulli’s equation approach. The current model specializes in discerning the propagation of optical soliton pulses within optical fibers. Obtaining the optical solutions for this model, particularly the sextic power, is an essential yet challenging task. To generate the nonlinear ordinary differential equation, we insert the complex wave transformations into the present time-fractional nonlinear Schrödinger equations. Here, a system of linear equations in polynomial form using the proposed approach is acquired. By solving the linear system of equations, various solution sets were generated, each containing different values for the parameters of the studied equation. Additionally, the process yielded distinct approaches for solving the problem. Several novel optical soliton solutions are constructed for the time-fractional Schrödinger equation with the Kudryashov nonlinear refractive index, and the obtained soliton solutions satisfy the model. The visual representations of the obtained solution functions through contour, three-dimensional, and two-dimensional depictions in various simulations are shown, as presented in the figures. The results suggest that the employed methods are efficient and powerful tools to be applied to various differential equations with fractional and integer orders.