Integrability of invariant metrics on the diffeomorphism group of the circle

Abstract : Each Hk Sobolev inner product 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 relatively to a modified Lie-Poisson structure.
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Adrian Constantin, Boris Kolev. Integrability of invariant metrics on the diffeomorphism group of the circle. Journal of Nonlinear Science, Springer Verlag, 2006, 16, pp.109-122. ⟨10.1007/s00332-005-0707-4⟩. ⟨hal-00095916⟩

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