Proof of the Treves theorem on the KdV hierarchy  [ Preuve du théorème de Treves pour la hiérarchie KdV ]
Annales de l'Institut Fourier, Tome 55 (2005) no. 6, p. 2015-2023
Une nouvelle et plus courte démonstration du théorème de Treves sur un critère algébrique pour les premières intégrales de la hiérarchie KdV est donnée, ainsi qu'une addition au théorème.
A new, shorter, proof of the Treves theorem on an algebraic criterion for the first integrals of the KdV hierarchy is given, along with an addition to the theorem.
DOI : https://doi.org/10.5802/aif.2149
Classification:  35Q53
Mots clés: KdV, premières intégrales, Treves
@article{AIF_2005__55_6_2015_0,
     author = {Dickey, Leonid},
     title = {Proof of the Treves theorem on the KdV hierarchy},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {55},
     number = {6},
     year = {2005},
     pages = {2015-2023},
     doi = {10.5802/aif.2149},
     zbl = {1078.35102},
     mrnumber = {2187943},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2005__55_6_2015_0}
}
Dickey, Leonid. Proof of the Treves theorem on the KdV hierarchy. Annales de l'Institut Fourier, Tome 55 (2005) no. 6, pp. 2015-2023. doi : 10.5802/aif.2149. http://www.numdam.org/item/AIF_2005__55_6_2015_0/

[1] F. Treves An algebraic characterization of the Korteweg - de Vries hierarchy., Duke Math. J., Tome 108 (2001) no. 2, pp. 251-294 | Article | MR 1833392 | Zbl 1028.37040

[2] L. A. Dickey On a generalization of the Treves criterion for the first integrals of the KdV hierarchy to higher GD hierarchies., Lett. Math. Phys., Tome 65 (2003), pp. 187-197 | Article | MR 2033705 | Zbl 1042.37050

[3] L. A. Dickey Soliton Equations and Hamiltonian Systems, 2nd Ed., World Scientific, Advanced Series in Mathematical Physics, Tome 26 (2003) | MR 1964513 | Zbl 01843266