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arXiv · 1302.0148

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

Alberto De Sole·Victor G. Kac
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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.

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Alberto De Sole, Victor G. Kac. 2013-02-01. Non-local Poisson structures and applications to the theory of integrable systems. https://doi.org/10.1007/s11537-013-1306-z

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