AI Insight
This study presents analytical solutions for needle-type solitons within a M-fractional paraxial wave equation framework, employing mathematical techniques to construct exact closed-form solutions. The research investigates the dynamics of these localized wave structures by applying fractional calculus, specifically the M-truncated fractional derivative, to model paraxial wave propagation in nonlinear optical media. Dynamical analysis, including stability assessment and phase portrait examination, is conducted to characterize the behavior of the obtained soliton solutions under varying fractional parameters.
Why it matters
Needle-type solitons and their fractional modeling have direct relevance to optical fiber communications, laser beam engineering, and photonic device design, where controlling light propagation at small scales is essential. Understanding fractional-order effects on soliton dynamics may improve the accuracy of models used in designing next-generation optical transmission systems.