Finite-gap Solutions of the Vortex Filament Equation, I

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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.
36 pages, 8 figures; additional references included

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Exactly Solvable and Integrable Systems, Differential Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/80882

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/nlin/0411065
 http://arxiv.org/abs/nlin/0411065

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arXiv