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The geodesic Vlasov equation and its integrable moment closures

Holm, DD and Tronci, C (2009) The geodesic Vlasov equation and its integrable moment closures Journal of Geometric Mechanics, 1 (2). pp. 181-208.

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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 for both the one- and two-component Camassa-Holm systems. The present paper extends our earlier work to recover another integrable system of ODE's that was recently introduced by Bloch and Iserles. Solutions of the Bloch-Iserles system are found to arise from the Klimontovich solution of the geodesic Vlasov equation. These solutions are shown to form one of the legs of a dual pair of momentum maps. The Lie-Poisson structures for the dynamics of truncated moment hierarchies are also presented in this context.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Holm, DD
Date : 4 February 2009
DOI : 10.3934/jgm.2009.1.181
Related URLs :
Depositing User : Symplectic Elements
Date Deposited : 17 May 2017 12:21
Last Modified : 10 Jun 2019 13:08

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