GENERALIZATION OF HASIMOTO'S TRANSFORMATION

Abstract

In this paper, we generalize the famous Hasimoto's transformation by showing that the dynamics of a closed unidimensional vortex filament embedded in a three-dimensional manifold M of constant curvature, gives rise under Hasimoto's transformation to the nonlinear Schrödinger equation. We also give a natural interpretation of the function ψ introduced by Hasimoto in terms of moving frames associated to a natural complex bundle over the filament.

Locations

• International Journal of Geometric Methods in Modern Physics - View
• arXiv (Cornell University) - PDF