Non-local Poisson structures and applications to the theory of integrable systems
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Kac_Non-local poisson.pdf
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885.01 KB
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Author(s)
De Sole, Alberto
Kac, Victor
Date Issued
September 2013
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s11537-013-1306-z
