Finite-gap Solutions of the Vortex Filament Equation, I

Details Finite-gap Solutions of the Vortex Filament Equation, I Finite-gap Solutions of the Vortex Filament Equation, I

2004-11-30

arxiv.org/abs/nlin/0411065v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

36 pages, 8 figures; additional references included

Scientific paper

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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