Generalization of Hasimoto's transformation
Differential Geometry
2012-04-25 v1
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 of constant curvature gives rise under Hasimoto's transformation to the non-linear Schrodinger equation. We also give a natural interpretation of the function \psi introduced by Hasimoto in terms of moving frames associated to a natural complex bundle over the filament.
Cite
@article{arxiv.1204.5324,
title = {Generalization of Hasimoto's transformation},
author = {Mathieu Molitor},
journal= {arXiv preprint arXiv:1204.5324},
year = {2012}
}