Geodesic flows on diffeomorphism groups with Sobolev metrics and integrable systems
It is well-known that the hydrodynamics on an incompressible ideal fluid can be described by the geodesic flow on the group of volume preserving transformations with respect to a certain right invariant metric. In this paper the author shows that the supersymmetric Harry-Dym equation can be also described by geodesic motions on the Bott-Virasoro group, which is an extension of the group of diffeomorphisms on the circle.
scientific article; zbMATH DE number 1845289