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

Annalisa M. Calini·Thomas A. Ivey
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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.

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Annalisa M. Calini, Thomas A. Ivey. 2006-12-29. Finite-gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations. https://doi.org/10.1007/s00332-007-9002-x

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