## Non-local Poisson structures and applications to the theory of integrable systems    [PDF]

Alberto De Sole, Victor G. Kac
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.
View original: http://arxiv.org/abs/1302.0148