Geodesic Flow and Two (Super) Component Analog of the Camassa-Holm Equation - Guha, P.; Olver, P.J. (Symmetry, Integrability and Geometry: Methods and Applications, 2006)
We derive the 2-component Camassa-Holm equation and corresponding N = 1 super generalization as geodesic flows with respect to the H1 metric on the extended Bott-Virasoro and superconformal groups, respectively.