On the bi-Hamiltonian structures of the Camassa-Holm and Harry Dym equations

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dc.creatorLorenzoni, Paolo
dc.creatorPedroni, Marco
dc.date2004-07-26
dc.date2004-10-04
dc.date.accessioned2026-07-07T05:35:50Z
dc.date.available2026-07-07T05:35:50Z
dc.descriptionWe show that the bi-Hamiltonian structures of the Camassa-Holm and Harry Dym hierarchies can be obtained by applying a reduction process to a simple Poisson pair defined on the loop algebra of $\mathfrak{sl}(2,\mathbb{R})$. The reduction process is a bi-Hamiltonian reduction, that can be canonically performed on every bi-Hamiltonian manifold.
dc.description11 pages, LaTeX; minor changes, to appear in Int. Math. Res. Not
dc.identifierhttps://arxiv.org/abs/nlin/0407057
dc.identifierhttp://arxiv.org/abs/nlin/0407057
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/80788
dc.subjectExactly Solvable and Integrable Systems
dc.subjectDifferential Geometry
dc.titleOn the bi-Hamiltonian structures of the Camassa-Holm and Harry Dym equations
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