Comptes Rendus
no. 7
Lie algebras/Partial differential equations
Compatible Hamiltonian operators for the Krichever–Novikov equation
[Opérateurs hamiltoniens compatibles pour l'équation de Krichever–Novikov]

Présenté par : Michèle Vergne

Sylvain Carpentier1
1 Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Comptes Rendus. Mathématique, Volume 355 (2017) no. 7, pp. 744-747.

Il a été démontré par Sokolov que la hiérarchie de l'équation de Krichever–Novikov est hamiltonienne pour l'opérateur hamiltonien H0=ux∂−1ux et possède deux opérateurs de récursion faiblement non locaux de degrés 4 et 6, L4 et L6. Nous montrons ici que H0, L4H0 et L6H0 sont des opérateurs hamiltoniens compatibles pour lesquels la hiérarchie de l'équation de Krichever–Novikov est hamiltonienne.

It has been proved by Sokolov that Krichever–Novikov equation's hierarchy is hamiltonian for the Hamiltonian operator H0=ux∂−1ux and possesses two weakly non-local recursion operators of degrees 4 and 6, L4 and L6. We show here that H0, L4H0 and L6H0 are compatible Hamiltonians operators for which the Krichever–Novikov equation's hierarchy is hamiltonian.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.05.009

Sylvain Carpentier 1

1 Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 
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Sylvain Carpentier. Compatible Hamiltonian operators for the Krichever–Novikov equation. Comptes Rendus. Mathématique, Volume 355 (2017) no. 7, pp. 744-747. doi : 10.1016/j.crma.2017.05.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.05.009/

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  • Igor Krichever; Nikita Nekrasov Novikov-Veselov symmetries of the two-dimensional O(N) sigma model, SIGMA. Symmetry, Integrability and Geometry: Methods and Applications, Volume 18 (2022), p. paper | DOI:10.3842/sigma.2022.006 | Zbl:1479.14040

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