Integrability of invariant metrics on the diffeomorphism group of the circle

Adrian Constantin, Boris Kolev

Published 2009-11-26Version 1

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.