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VOL. 7 | 2006 Geometry and Topology of Finite-Gap Vortex Filaments

Abstract

In this talk, I will discuss the vortex filament flow, and its connection with the nonlinear Schrödinger equation (NLS), the geometry of solutions to the filament flow that correspond to finite-gap solutions of NLS, and in particular, the relationship between geometric properties of the filament to features of the Floquet spectrum of a periodic NLS potential. These will be illustrated by the example of elastic rod centerlines. I will also discuss the geometric implications of symmetric Floquet spectra, and the topological implications of certain isoperiodic deformations of the spectrum that open up real double points.

Information

Published: 1 January 2006
First available in Project Euclid: 13 July 2015

zbMATH: 1132.53005
MathSciNet: MR2228372

Digital Object Identifier: 10.7546/giq-7-2006-187-202

Rights: Copyright © 2006 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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