148 citations · 348 across the 12 of their papers we have counts for
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nlin.SI2009★ 34 cited
The geodesic Vlasov equation and its integrable moment closures
Darryl D. Holm, Cesare Tronci
Various integrable geodesic flows on Lie groups are shown to arise by taking moments of a geodesic Vlasov equation on the group of canonical transformations. This was already known…
nlin.SI2008★ 37 cited
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…
nlin.SI2007★ 38 cited
Vlasov moments, integrable systems and singular solutions
John Gibbons, Darryl D Holm, Cesare Tronci
The Vlasov equation for the collisionless evolution of the single-particle probability distribution function (PDF) is a well-known Lie-Poisson Hamiltonian system. Remarkably, the o…