(untitled) (Contemporary Mathematics, 2025)
This study explores novel quiescent optical soliton solutions to the Radhakrishnan-Kundu-Lakshmanan (RKL)equation, a significant model in nonlinear optics. Utilizing three distinct analytical methods, which are the modified extended Tanh-function method, the addendum to Kudryashov method, and the Kudryashov’s auxiliary equation method, we derive an array of new quiescent optical soliton solutions, including dark, singular, bright, and bright-dark solitons. The novelty of this work lies in the comprehensive application of these advanced techniques to uncover previously unreported quiescent optical soliton profiles, revealing the inherent diversity and richness of the RKL equation’s solution space. The physical significance of these solutions is highlighted through detailed two-dimensional visualizations, offering deeper insights into their structural characteristics and potential implications in nonlinear optics. This work not only expands new analytical perspectives for solving the RKL equation but also contributes to a broader understanding of soliton wave phenomena in complex nonlinear systems.