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

@article{Sole2013NonlocalPS, title={Non-local Poisson structures and applications to the theory of integrable systems}, author={A. Sole and V. Kac}, journal={Japanese Journal of Mathematics}, year={2013}, volume={8}, pages={233-347} }

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.

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