Fibration of the phase space for the Korteweg-de Vries equation
Annales de l'Institut Fourier, Volume 41 (1991) no. 3, p. 539-575

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.

Dans cet article on démontre que la fibration de L 2 (S 1 ) par des potentiels isospectraux pour l’équation de Schrödinger périodique à une dimension est triviale. Ce résultat peut être appliqué aux solutions de N 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},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {41},
     number = {3},
     year = {1991},
     pages = {539-575},
     doi = {10.5802/aif.1265},
     zbl = {0731.58033},
     mrnumber = {92k:58212},
     language = {en},
     url = {http://www.numdam.org/item/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/item/AIF_1991__41_3_539_0/

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