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On Action-Angle Variables¶for the Second Poisson Bracket of KdV

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Abstract:

We prove that on the Sobolev spaces H N(S 1) (N≥ 0), each leaf of the foliation, induced by the second Poisson bracket of KdV, admits global action-angle variables. The actions with respect to the first bracket raise to the actions with respect to the second bracket. The angles for the first bracket are, at the same time, angles for the second bracket.

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  1. Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland. E-mail: tk@math.unizh.ch, , , , , , CH

    T. Kappeler & M. Makarov

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  1. T. Kappeler
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  2. M. Makarov
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Received: 12 November 1999 / Accepted: 9 May 2000

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Kappeler, T., Makarov, M. On Action-Angle Variables¶for the Second Poisson Bracket of KdV. Commun. Math. Phys. 214, 651–677 (2000). https://doi.org/10.1007/s002200000282

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  • DOI: https://doi.org/10.1007/s002200000282

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