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On the symplectic phase space of KdV

Authors: T. Kappeler, F. Serier and P. Topalov
Journal: Proc. Amer. Math. Soc. 136 (2008), 1691-1698
MSC (2000): Primary 35Q53, 34K17
Published electronically: November 30, 2007
MathSciNet review: 2373598
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Abstract: We prove that the Birkhoff map $ \Omega$ for KdV constructed on $ H^{-1}_0(\mathbb{T})$ can be interpolated between $ H^{-1}_0(\mathbb{T})$ and $ L^2_0(\mathbb{T})$. In particular, the symplectic phase space $ H^{1/2}_0(\mathbb{T})$ can be described in terms of Birkhoff coordinates.

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T. Kappeler
Affiliation: Mathematics Institute, University of Zurich, Winterthurerstr. 190, 8057 Zurich, Switzerland

F. Serier
Affiliation: Ecole Centrale de Lyon, Institut C. Jordan, UMR CNRS 5208, 36 avenue Guy de Collongue, 69134 Ecully, Cedex, France

P. Topalov
Affiliation: Department of Mathematics, Northeastern University, 360 Huntington Ave., Boston, Massachusetts 02115

Received by editor(s): December 21, 2006
Received by editor(s) in revised form: January 1, 2018, and January 1, 2007
Published electronically: November 30, 2007
Additional Notes: The first author was supported in part by the Swiss National Science Foundation, the programme SPECT, and the European Community through the FP6 Marie Curie RTN ENIGMA (MRTN-CT-2004-5652).
Communicated by: Walter Craig
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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