Magnetic vortices
M. Barros, Alfonso Romero · Europhysics Letters (EPL) · 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.