Levin Maier
Introducing the magnetic Euler-Arnold equation
In this note, we combine V. Arnolds celebrated approach through the nowadays so called Euler-Arnold equation on the geodesic equation on an Lie group equipped with an right invariant metric and his approach on the motion of charged particle in a magnetic field, by introducing the magnetic Euler-Arnold equation, this is the Eulerian form of the magnetic geodesic flow of an infinite dimensional magnetic system on a Lie group equipped with an right invariant metric and right invariant closed two form as magnetic field. As an illustration, we show that the KdV equation, generalized Camassa-Holm equation and the infinite conductivity equation are magnetic Euler-Arnold equations.
