Integrability of invariant metrics on the diffeomorphism group of the circle

Details Integrability of invariant metrics on the diffeomorphism group of the circle Integrability of invariant metrics on the diffeomorphism group of the circle

2009-11-26

arxiv.org/abs/0911.5058v1

Journal of Nonlinear Science 16 (2006) 109-122

Physics

Mathematical Physics

Scientific paper

10.1007/s00332-005-0707-4

Each H^k Sobolev inner product defines a Hamiltonian vector field X_k on the
regular dual of the Lie algebra of the diffeomorphism group of the circle. We
show that only X_0 and X_1 are bi-Hamiltonian relatively to a modified
Lie-Poisson structure.

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