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JNS
2007

Finite-Gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations

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Finite-Gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations
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.
A. Calini, T. Ivey
Added 15 Dec 2010
Updated 15 Dec 2010
Type Journal
Year 2007
Where JNS
Authors A. Calini, T. Ivey
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