Optical soliton solutions for a generalized nonlocal nonlinear Schrödinger-type equation with Kudryashov-like refractive index law

This study explores a perturbed nonlinear optical system governed by Kudryashov’s law with an arbitrary refractive index to derive novel optical soliton solutions. Three distinct analytical techniques are employed to obtain a broad class of exact solutions for the governing equations: The simplest equation method, Kudryashov’s integration scheme, and the extended auxiliary equation integration scheme. Through these approaches, multiple families of optical soliton solutions are constructed, including bright, dark, composite, and breather-type solitons, as well as singular periodic and singular soliton wave structures. The physical characteristics and dynamical behaviors of these solitons are visualized through graphical representations, providing insights into the effects of system parameters and perturbations. Furthermore, constraint conditions are derived to ensure the mathematical consistency and physical validity of the obtained solutions. The results highlight the effectiveness and flexibility of the implemented algorithms and offer a useful analytical framework for investigating nonlinear optical wave propagation in complex media.