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Integrability of Invariant Metrics on the Diffeomorphism Group of the Circle

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Abstract

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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Authors and Affiliations

  1. Trinity College, Department of Mathematics, Dublin 2, Ireland

    A. Constantin

  2. CMI, 39, rue F. Joliot-Curie, 13453 Marseille Cedex 13, France

    B. Kolev

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  1. A. Constantin
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  2. B. Kolev
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Correspondence to A. Constantin or B. Kolev.

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Constantin, A., Kolev, B. Integrability of Invariant Metrics on the Diffeomorphism Group of the Circle. J Nonlinear Sci 16, 109–122 (2006). https://doi.org/10.1007/s00332-005-0707-4

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  • DOI: https://doi.org/10.1007/s00332-005-0707-4

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