Integrable dynamics of knotted vortex filaments. (English) Zbl 1066.37049
Mladenov, Ivaïlo 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 (ISBN 954-84952-8-7/pbk). 11-50 (2004).
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. For the entire collection see [Zbl 1048.53002
|37N10||Dynamical systems in fluid mechanics, oceanography and meteorology|
|37K10||Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies|
|37K25||Relations of infinite-dimensional systems with differential geometry|
|35Q53||KdV-like (Korteweg-de Vries) equations|
|53C44||Geometric evolution equations (mean curvature flow, Ricci flow, etc.)|