Non-local Poisson structures and applications to the theory of
integrable systems [PDF]
Alberto De Sole, Victor G. KacWe 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
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