Optical modeling of Hasimoto map for antiferromagnetic timelike optical fiber

Abstract

In this study, we study optical hasimoto map corresponds to under the quasi-frame for timelike curves in 3D Minkowski space. We investigate the relationship of this transformation with some flow equations, which are known examples for nonlinear optical systems. Here, we first obtain the q-Hasimoto map as equivalent of the Hasimoto map in the q-frame for timelike space curve in 3D Minkowski Space. Then, we examine the effect on the q-Hasimoto map of the some flow equations such as vortex filament equation, Heisenberg antiferromagnetic flow. Finally, we present comments on some of the physical consequences of these effects that we have examined.