Finite-gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations
Exactly Solvable and Integrable Systems
2009-11-11 v1 Differential Geometry
Abstract
We study the topology of quasiperiodic solutions of the vortex filament equation in a neighborhood of multiply covered circles. We construct these solutions by means of a sequence of isoperiodic deformations, at each step of which a real double point is "unpinched" to produce a new pair of branch points and therefore a solution of higher genus. We prove that every step in this process corresponds to a cabling operation on the previous curve, and we provide a labelling scheme that matches the deformation data with the knot type of the resulting filament.
Keywords
Cite
@article{arxiv.nlin/0612065,
title = {Finite-gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations},
author = {Annalisa M. Calini and Thomas A. Ivey},
journal= {arXiv preprint arXiv:nlin/0612065},
year = {2009}
}
Comments
33 pages, 5 figures; submitted to Journal of Nonlinear Science