%0 Journal Article
%T Finite-gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations
%A Annalisa M. Calini
%A Thomas A. Ivey
%J Physics
%D 2006
%I arXiv
%R 10.1007/s00332-007-9002-x
%X 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.
%U http://arxiv.org/abs/nlin/0612065v1