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Zbl 1066.37049
Calini, Annalisa
Integrable dynamics of knotted vortex filaments. (English)
[A] Mladenov, Iva\"ilo M. (ed.) et al., Proceedings of the 5th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 5--12, 2003. Sofia: Bulgarian Academy of Sciences. 11-50 (2004). ISBN 954-84952-8-7/pbk

This series of lectures adresses relationships between integrability (the Floquet spectrum of a given solution), geometry and topology of closed curve solutions of the vortex flament equation. Among others, the author discusses the explicit algebro-geometric construction of $N$-phase solutions of the vortex flament equation, following Krichever's use of the Baker-Akhiezer function.
[Messoud A. Efendiev (Berlin)]

MSC 2000:: *37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
37K10 Completely integrable systems etc.
37K25 Relations with differential geometry
35Q53 KdV-like equations
76B47 Vortex flows
53C44 Geometric evolution equations (mean curvature flow)

Keywords: integrability; Floquet spectrum; vortex flament equation; $N$-phase solutions

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