Integrable invariant Sobolev metrics on the Abelian extension of the diffeomorphism group of the circle and two-component generalizations of the Camassa-Holm equation

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dc.creatorKuzmin, P. A.
dc.date2006-10-26
dc.date2007-03-26
dc.date.accessioned2026-07-07T07:53:39Z
dc.date.available2026-07-07T07:53:39Z
dc.descriptionIn this note we classify some integrable invariant Sobolev metrics on the Abelian extension of the diffeomorphism group of the circle. We also derive a new two-component generalization of the Camassa-Holm equation. The system obtained appears to be unique bi-Hamiltonian flow on the coadiont obrit of $\Diff_+(S^1)\ltimes C^\infty(S^1)$ generalizes the Camassa-Holm flow on $\Vect(S^1)^*$.
dc.descriptionadded references
dc.identifierhttps://arxiv.org/abs/math/0610786
dc.identifierhttp://arxiv.org/abs/math/0610786
dc.identifierMath. Notes 81, 149--152 (2007)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/126302
dc.subjectSymplectic Geometry
dc.subjectMathematical Physics
dc.titleIntegrable invariant Sobolev metrics on the Abelian extension of the diffeomorphism group of the circle and two-component generalizations of the Camassa-Holm equation
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