(untitled) (Contemporary Mathematics, 2023)
The study undertakes a comprehensive exploration of optical solitons within the context of the dispersive concatenation model, utilizing three distinct integration algorithms. These approaches, namely the enhanced Kudryashov’ s method, the Riccati equation expansion approach, and the Weierstrass’ expansion scheme, offer distinct perspectives and insights into the behavior of optical solitons. By employing the enhanced Kudryashov’ s approach, the research uncovers a spectrum of soliton solutions, including straddled, bright, and singular optical solitons. This algorithm not only provides a nuanced understanding of the various soliton types but also highlights the occurrence of singular solitons that exhibit unique characteristics. The Riccati equation expansion approach, on the other hand, yields dark solitons in addition to singular solitons. This particular method expands our comprehension of soliton behavior by encompassing the presence of dark solitons alongside singular ones. This diversification contributes to a more comprehensive grasp of soliton phenomena. Furthermore, the application of the Weierstrass’ expansion scheme extends the analysis to encompass bright, singular, and other variations of straddled solitons. This method introduces further complexity and diversity to the optical soliton. Importantly, the study meticulously addresses the parameter constraints that govern the behavior of these solitons. By providing a comprehensive presentation of these constraints, the research enhances the practical applicability of the findings, offering insights into the conditions under which these soliton solutions emerge.