148 citations · 1.1k across the 66 of their papers we have counts for
4 papers · 1 filter
Singular solutions of a modified two-component Camassa-Holm equation
Darryl D. Holm, Lennon Ó Náraigh, Cesare Tronci
The Camassa-Holm equation (CH) is a well known integrable equation describing the velocity dynamics of shallow water waves. This equation exhibits spontaneous emergence of singular…
Geodesic flows on semidirect-product Lie groups: geometry of singular measure-valued solutions
Darryl D. Holm, Cesare Tronci
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 re…
Geometric dynamics of Vlasov kinetic theory and its moments
Cesare Tronci
The Vlasov equation of kinetic theory is introduced and the Hamiltonian structure of its moments is presented. Then we focus on the geodesic evolution of the Vlasov moments. As a f…
Geometry of Vlasov kinetic moments: a bosonic Fock space for the symmetric Schouten bracket
John Gibbons, Darryl D Holm, Cesare Tronci
The dynamics of Vlasov kinetic moments is shown to be Lie-Poisson on the dual Lie algebra of symmetric contravariant tensor fields. The corresponding Lie bracket is identified with…