Geodesic Equations on Diffeomorphism Groups - Vizman, C. (Symmetry, Integrability and Geometry: Methods and Applications, 2008)
We bring together those systems of hydrodynamical type that can be written as geodesic equations on diffeomorphism groups or on extensions of diffeomorphism groups with right invariant L² or H¹ metrics. We present their formal derivation starting from Euler's equation, the first order equation satisfied by the right logarithmic derivative of a geodesic in Lie groups with right invariant metrics.