Differential Geometry of the Vortex Filament Equation
High Energy Physics - Theory
2015-06-26 v1
Abstract
Differential calculus on the space of asymptotically linear curves is developed. The calculus is applied to the vortex filament equation in its Hamiltonian description. The recursion operator generating the infinite sequence of commuting flows is shown to be hereditary. The system is shown to have a description with a Hamiltonian pair. Master symmetries are found and are applied to deriving an expression of the constants of motion in involution. The expression agrees with the inspection of Langer and Perline.
Keywords
Cite
@article{arxiv.hep-th/9611073,
title = {Differential Geometry of the Vortex Filament Equation},
author = {Yukinori Yasui and Norihito Sasaki},
journal= {arXiv preprint arXiv:hep-th/9611073},
year = {2015}
}
Comments
20 pages, LaTeX, no figures