Novel approaches to the construction of solitons in Fokas fiber-optic models

The Fokas system plays a pivotal role in modeling nonlinear pulse propagation through monomode optical fibers, with exact solutions offering critical insights into the physical mechanisms governing excitation instability. In this study, we introduce two novel function transformation techniques to analytically resolve the Riccati equation, enabling the derivation of previously unidentified closed-form solutions. By employing the Riccati equation as an auxiliary framework, we systematically solve the Fokas system and generate an extensive family of solitary wave solutions. Notably, through systematic variation of coefficients in the Riccati equation, we uncover an unprecedented diversity of localized wave configurations, including previously unreported profiles absent from existing literature. These findings significantly enhance the understanding of nonlinear dynamics in the Fokas system while expanding the methodological toolkit for analyzing optical fiber propagation phenomena. The proposed solutions not only validate theoretical predictions but also provide a foundation for experimental verification and photonic device design.