Non-local Poisson structures and applications to the theory of integrable systems
Mathematical Physics
2015-12-18 v2 math.MP
Rings and Algebras
Representation Theory
Exactly Solvable and Integrable Systems
Abstract
We develop a rigorous theory of non-local Poisson structures, built on the notion of a non-local Poisson vertex algebra. As an application, we find conditions that guarantee applicability of the Lenard-Magri scheme of integrability to a pair of compatible non-local Poisson structures. We apply this scheme to several such pairs, proving thereby integrability of various evolution equations, as well as hyperbolic equations.
Keywords
Cite
@article{arxiv.1302.0148,
title = {Non-local Poisson structures and applications to the theory of integrable systems},
author = {Alberto De Sole and Victor G. Kac},
journal= {arXiv preprint arXiv:1302.0148},
year = {2015}
}
Comments
120 pages. This paper is an edited version of the merger of the two papers with archive numbers arXiv:1210.1688 and arXiv:1211.2391. Version 2: minor corrections. Added keywords and MSC codes. To appear in the Japanese Journal of Mathematics