An investigation of optical solitons of the fractional cubic-quintic nonlinear pulse propagation model: an analytic approach and the impact of fractional derivative

This study focuses on investigating analytical soliton solutions within the context of the time-fractional cubic-quintic nonlinear non-paraxial pulse propagation model, an adaptive model with extensive uses in various intricate real phenomena, such as nonlinear optics, fiber optics communication, optical signal processing, laser-tissue interaction in biomedical science, among others. Depending on the strength of the cubic and quintic nonlinear terms, various nonlinear effects, including self-focusing, self-phase modulation, and wave mixing, can be observed. This model is investigated using a powerful analytical technique, the (G^'/G, 1/G) -expansion approach, which develops several potential solitons that allow for insight into the laser pulse interactions. This study yields diverse illustrative soliton solutions, including periodic, bell-shaped, kink, singular solitons, etc. some of which have been documented in former literature. Furthermore, we conduct an extensive analysis of these solitons, considering both anomalous and normal group velocity dispersion, and effectively visualize the results through two- and three-dimensional graphs, along with contour plots. The findings in this article could hold significance for researchers engaged in the advancement of optical equipment, biomedical laser devices, mode-locked lasers, and similar technologies.