Optical recursion systems for the Hasimoto map and optical applications with spherical frame

Abstract

In this research, we analyze the Hasimoto map and some flow equations for spherical frame (s-frame) in S-2 spherical space. Here, we first obtain Hasimoto map, which we call the s- Hasimoto map, for the s-frame in S-2. Then, we get some soliton equations with the help of s-Hasimoto map and vortex filament (Da Rios) equation. Later, by examining the effects of visco-Da Rios equation and visco-Landau Lifshitz equation on s-Hasimoto map, we obtain some flow equations. Finally, we present some of the contributions that all our results will make to magnetic fluxes, fluid dynamics and, especially, optical motion.