Open Access
VOL. 5 | 2004 Integrable Dynamics of Knotted Vortex Filaments
Annalisa Calini

Editor(s) Ivaïlo M. Mladenov, Allen C. Hirshfeld

Geom. Integrability & Quantization, 2004: 11-50 (2004) DOI: 10.7546/giq-5-2004-11-50


The dynamics of vortex filaments has provided for almost a century one of the most interesting connections between differ ential geometry and soliton equations, and an example in which knotted curves arise as solutions of differential equations possessing an infinite family of symmetries and a remarkably rich geometrical structure. These lectures discuss several aspects of the integrable dynamics of closed vortex filaments in an Eulerian fluid, including its Hamiltonian formulation, the construction of a large class of special solutions, and the role of the Floquet spectrum in characterizing the geometric and topological properties of the evolving curves.


Published: 1 January 2004
First available in Project Euclid: 12 June 2015

zbMATH: 1066.37049
MathSciNet: MR2082293

Digital Object Identifier: 10.7546/giq-5-2004-11-50

Rights: Copyright © 2004 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences


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