Abstract This research establishes a comprehensive theoretical framework for soliton propagation in magneto-optic waveguides by investigating a generalized coupled Kudryashov-type nonlinear Schrödinger system under the influence of higher-order nonlinear effects. The primary objective is to resolve the complex interplay between self-steepening, nonlinear dispersion, and magnetization parameters, which are often oversimplified in standard models. By implementing the improved simple equation method, we derive a new spectrum of exact analytical solutions, including robust kink, antikink, and singular profiles, and provide their first detailed parametric characterization. Our findings demonstrate that tuning specific nonlinear coefficients allows for precise control over pulse stability and transition gradients, offering critical insights for the development of high-capacity optical communication architectures and all-optical switching technologies.
Tarek et al. (2026) studied this question.