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Fibration of the phase space for the Korteweg-de Vries equation


Kappeler, T (1991). Fibration of the phase space for the Korteweg-de Vries equation. Annales de l'institut Fourier, 41(3):539-575.

Abstract

In this article we prove that the fibration of $L^ 2(S^ 1)$ by potentials which are isospectral for the 1-dimensional periodic Schrödinger equation, is trivial. This result can be applied, in particular, to $N$-gap solutions of the Korteweg-de Vries equation (KdV) on the circle: one shows that KdV, a completely integrable Hamiltonian system, has global action-angle variables.

Abstract

In this article we prove that the fibration of $L^ 2(S^ 1)$ by potentials which are isospectral for the 1-dimensional periodic Schrödinger equation, is trivial. This result can be applied, in particular, to $N$-gap solutions of the Korteweg-de Vries equation (KdV) on the circle: one shows that KdV, a completely integrable Hamiltonian system, has global action-angle variables.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1991
Deposited On:18 Feb 2010 11:14
Last Modified:21 Feb 2018 08:27
Publisher:Association des Annales de l'Institut Fourier
ISSN:0373-0956
Additional Information:© 1991 Annales de L'Institut Fourier
OA Status:Hybrid
Publisher DOI:https://doi.org/10.5802/aif.1265
Official URL:http://aif.cedram.org/item?id=AIF_1991__41_3_539_0
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1136595
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0731.58033
http://www.numdam.org/item?id=AIF_1991__41_3_539_0

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