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Comptes Rendus Mathématique
Volume 355, n° 7
pages 744-747 (juillet 2017)
Doi : 10.1016/j.crma.2017.05.009
Received : 12 May 2017 ;  accepted : 30 May 2017
Compatible Hamiltonian operators for the Krichever–Novikov equation
Opérateurs hamiltoniens compatibles pour l'équation de Krichever–Novikov
 

Sylvain Carpentier
 Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 

Abstract

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

The full text of this article is available in PDF format.
Résumé

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

The full text of this article is available in PDF format.


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