Volume 77, Number 3, February 2007
|Number of page(s)||5|
|Section||Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics|
|Published online||02 February 2007|
Departamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada - 18071-Granada, Spain
Accepted: 30 November 2006
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.
PACS: 47.65.Cb – Magnetic fluids and ferrofluids / 47.32.C- – Vortex dynamics
© Europhysics Letters Association, 2007
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