In this article we prove that the fibration of by potentials which are isospectral for the 1-dimensional periodic Schrödinger equation, is trivial. This result can be applied, in particular, to -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.
Dans cet article on démontre que la fibration de par des potentiels isospectraux pour l’équation de Schrödinger périodique à une dimension est triviale. Ce résultat peut être appliqué aux solutions de lacunes de l’équation de Korteweg-de Vries (KDV) sur le cercle : on en déduit que KdV — un système hamiltonien complètement intégrable — a des variables action-angle globales.
@article{AIF_1991__41_3_539_0, author = {Kappeler, Thomas}, title = {Fibration of the phase space for the {Korteweg-de} {Vries} equation}, journal = {Annales de l'Institut Fourier}, pages = {539--575}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {41}, number = {3}, year = {1991}, doi = {10.5802/aif.1265}, mrnumber = {92k:58212}, zbl = {0731.58033}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1265/} }
TY - JOUR AU - Kappeler, Thomas TI - Fibration of the phase space for the Korteweg-de Vries equation JO - Annales de l'Institut Fourier PY - 1991 SP - 539 EP - 575 VL - 41 IS - 3 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.1265/ DO - 10.5802/aif.1265 LA - en ID - AIF_1991__41_3_539_0 ER -
%0 Journal Article %A Kappeler, Thomas %T Fibration of the phase space for the Korteweg-de Vries equation %J Annales de l'Institut Fourier %D 1991 %P 539-575 %V 41 %N 3 %I Institut Fourier %C Grenoble %U http://www.numdam.org/articles/10.5802/aif.1265/ %R 10.5802/aif.1265 %G en %F AIF_1991__41_3_539_0
Kappeler, Thomas. Fibration of the phase space for the Korteweg-de Vries equation. Annales de l'Institut Fourier, Volume 41 (1991) no. 3, pp. 539-575. doi : 10.5802/aif.1265. http://www.numdam.org/articles/10.5802/aif.1265/
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