On the optical soliton solutions of the perturbed Fokas–Lenells equation having parabolic law of self-phase modulation in the presence of spatio-temporal dispersion

In this study, we aimed to obtain optical soliton solutions of the perturbed Fokas–Lenells equation having the parabolic law of self-phase modulation in the presence of spatio-temporal dispersion. The Fokas–Lenells equation is significant in nonlinear optics, particularly for modeling femto-second pulse propagation. By implementing the enhanced Kudryashov method, we derive dark, bright, and kink optical solitons for the investigated model. Visualizing the obtained results supported by 3D and 2D simulations and examining the effects of the parameters within the model on the soliton behavior constitute the other branches of the study. Considering that the interaction of various self-phase modulation forms with the chromatic dispersion term is different and its effects on soliton behavior are different, the parabolic law nonlinearity form is examined in the study and the results obtained are aimed at contributing to studies on both the model and nonlinear optics.