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Geodesic flows on semidirect-product Lie groups: geometry of singular measure-valued solutions
Proceedings of the Royal Society A
The EPDiff equation (or dispersionless Camassa-Holm equation in 1D) is a well known example of geodesic motion on the Diff group of smooth invertible maps (diffeomorphisms). Its recent two-component extension governs geodesic motion on the semidirect product Diff F, where F denotes the space of scalar functions. This paper generalizes the second construction to consider geodesic motion on Diffg, where g denotes the space of scalar functions that take values on a certain Lie algebra (fordoi:10.1098/rspa.2008.0263 fatcat:4yrh5ikgsregbh46duhz5srf54