Volume 77, Number 3, February 2007
Article Number 34002
Number of page(s) 5
Section Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics
Published online 02 February 2007
EPL, 77 (2007) 34002
DOI: 10.1209/0295-5075/77/34002

Magnetic vortices

M. Barros and A. Romero

Departamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada - 18071-Granada, Spain

received 9 October 2006; accepted in final form 30 November 2006; published February 2007
published online 2 February 2007

In spaces with constant curvature, magnetic trajectories of a Killing magnetic field are showed to be centerlines of Kirchhoff elastic rods. If the space is also simply connected, then a Killing magnetic flow is proved to be equivalent with the Kirchhoff elastic rod variational model. This allows to see Killing magnetic flows as vortex filament flows and so use the Hasimoto transformation to state the solitonic nature of the magnetic trajectories as solutions of the cubic Schrödinger equation.

47.65.Cb - Magnetic fluids and ferrofluids.
47.32.C- - Vortex dynamics.

© Europhysics Letters Association 2007