Optical modeling for geometric phase for the Hasimoto transformations on unit sphere

Abstract

In this paper, the key issue we address here is the Hasimoto transformation in three-dimensional Euclidean space, which allows us to specify the magnetic trajectory for the spherical curve in R-3. We, then show the motion of the spherical curve is equal to the nonlinear heat system. Lastly, we solve this nonlinear heat system numerically and then give a physical application of it.