# 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.

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 07 Faculty of Science > Institute of Mathematics 510 Mathematics English 1991 18 Feb 2010 11:14 05 Apr 2016 13:28 Association des Annales de l'Institut Fourier 0373-0956 © 1991 Annales de L'Institut Fourier http://aif.cedram.org/item?id=AIF_1991__41_3_539_0 http://www.ams.org/mathscinet-getitem?mr=1136595http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0731.58033http://www.numdam.org/item?id=AIF_1991__41_3_539_0
Permanent URL: https://doi.org/10.5167/uzh-22856

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