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

Author(s)
De Sole, Alberto; Kac, Victor
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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.
Date issued
2013-09
URI
http://hdl.handle.net/1721.1/92916
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Japanese Journal of Mathematics
Publisher
Springer-Verlag
Citation
De Sole, Alberto, and Victor G. Kac. “Non-Local Poisson Structures and Applications to the Theory of Integrable Systems.” Japanese Journal of Mathematics 8, no. 2 (September 2013): 233–347.
Version: Author's final manuscript
ISSN
0289-2316
1861-3624

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