Analysis of optical solitons for cubic-quintic nonlinear non-paraxial pulse propagation model

Abstract Herein, we study the exact soliton solution of the conformable cubic-quintic nonlinear non-paraxial pulse propagation equation for ultrashort pulse dynamics in the nonlinear optical world. While a considerable amount of research has focused on integer-order nonlinear models, relatively little has been done on solutions containing conformable fractional derivatives that have the potential to accurately represent dissipative optical systems. The main goal here is to compute complete families of exact traveling wave solutions from the generalized exponential rational function method (GERFM), and to study their stability. Using GERFM with specialized auxiliary function parameters, we effectively identify eight unique solution families covering various soliton structures expressed via hyperbolic and trigonometric functions. This results in various wave propagation behaviors that are validated in graphical representations in either a two-dimensional (2D) or three-dimensional (3D) framework. Specifically, variations in the conformable derivative order parameter $$\tau $$ exert a strong influence on soliton amplitude, width, and propagation velocity, demonstrating the superior capability of the conformable framework to model realistic dissipative effects compared to classical models. The gain spectrum characterization of steady-state solutions confirms the stability regions by analysis of their modulation instability. These are direct applications for generating dispersion-managed optical fiber communication systems, ultrafast laser pulse engineering, and nonlinear photonic devices. The originality of this work is that it applies GERFM in a complete manner with existing techniques on the conformable non-paraxial model, and provides a broad solution repository not encountered in the literature, promoting both theoretical and practical knowledge of nonlinear fiber optics.