Finite-gap Solutions of the Vortex Filament Equation, I

Annalisa Calini; Thomas Ivey

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arXiv · nlin/0411065

Finite-gap Solutions of the Vortex Filament Equation, I

Annalisa Calini·Thomas Ivey

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Abstract

For the class of quasi-periodic solutions of the vortex filament equation, we study connections between the algebro-geometric data used for their explicit construction and the geometry of the evolving curves. We give a complete description of genus one solutions, including geometrically interesting special cases such as Euler elastica, constant torsion curves, and self-intersecting filaments. We also prove generalizations of these connections to higher genus.

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Annalisa Calini, Thomas Ivey. 2004-12-02. Finite-gap Solutions of the Vortex Filament Equation, I. https://arxiv.org/abs/nlin/0411065

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