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. © 2013 The Mathematical Society of Japan and Springer Japan.
CITATION STYLE
De Sole, A., & Kac, V. G. (2013). Non-local Poisson structures and applications to the theory of integrable systems. Japanese Journal of Mathematics, 8(2), 233–347. https://doi.org/10.1007/s11537-013-1306-z
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