Analysis of optical soliton parameters and exact solutions in a generalized third-order nonlinear Schrödinger equation

Abstract In this paper, we explore optical solitons in a generalized third-order nonlinear Schrödinger equation (GNLSE) for ultrashort pulse propagation in nonlinear optical fibers. Using the collective variable (CV) method, we derive a system of ordinary differential equations that describes key soliton parameters, such as amplitude, width, chirp, and frequency. The numerical solutions obtained using the fourth-order Runge–Kutta algorithm show periodic oscillations of the aforementioned parameters. Another key result of the study is the discovery of bright soliton solutions using the semi-inverse method with fractal derivatives. We also demonstrate the effects of fractal parameters on the soliton solution with graphical simulations. Fractal dimensions (Ψ < 1) generate pulse irregularities that match experimental observations. The results clarify the interaction of higher-order effects, nonlinearity, and dispersion. In addition, the study’s findings highlight the importance of two methods used to improve data transmission in optical fibers and relate the theoretical analysis to potential real-world applications.