Integrability of Invariant Metrics on the Diffeomorphism Group of the Circle

Each Hk Sobolev inner product (k ≥ 0) defines a Hamiltonian vector field Xk on the regular dual of the Lie algebra of the diffeomorphism group of the circle. We show that only X0 and X1 are bi-Hamiltonian relative to a modified Lie-Poisson structure.

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Bibliographische Detailangaben
Veröffentlicht in:	Journal of nonlinear science 2006-04, Vol.16 (2), p.109-122
Hauptverfasser:	Constantin, A., Kolev, B.
Format:	Artikel
Sprache:	eng
Schlagworte:	Fields (mathematics) Isomorphism Lie groups Mathematical Physics Mathematics Physics Pilot projects
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	Each Hk Sobolev inner product (k ≥ 0) defines a Hamiltonian vector field Xk on the regular dual of the Lie algebra of the diffeomorphism group of the circle. We show that only X0 and X1 are bi-Hamiltonian relative to a modified Lie-Poisson structure.
ISSN:	0938-8974 1432-1467
DOI:	10.1007/s00332-005-0707-4