arXiv:1302.0148 Abstract | arXiv Analytics

arXiv:1302.0148 [math-ph]Abstract References Reviews Resources

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

Published 2013-02-01, updated 2013-07-17Version 2

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.

Comments: 120 pages. This paper is an edited version of the merger of the two papers with archive numbers arXiv:1210.1688 and arXiv:1211.2391. Version 2: minor corrections. Added keywords and MSC codes. To appear in the Japanese Journal of Mathematics

Categories: math-ph, math.MP, math.RA, math.RT, nlin.SI

Subjects: 37K10, 35Q53, 17B80, 17B69, 37K30, 17B63

Keywords: integrable systems, application, non-local poisson vertex algebra, compatible non-local poisson structures, evolution equations

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