Optical effects of some motion equations on quasi-frame with compatible Hasimoto map

Abstract

In this study, we examine the relationship between some equations of motion and the equations obtained by considering the differential formula of the quasi-Hasimoto map and some physical issues. Here, we first obtain the necessary equations of the quasi-Hasimoto transformation as the quasi-frame equivalent of the Hasimoto map. Then, we examine the relations between the vortex filament equation and the Landau–Lifshitz equation, which are important equations with soliton solutions, with the quasi-Hasimoto map. Finally, we interpret the connection of the results obtained as a result of these examinations with some physical issues. © 2021 Elsevier GmbH