Non-local Poisson structures and applications to the theory of integrable systems
Author(s)De Sole, Alberto; Kac, Victor
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Japanese Journal of Mathematics
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.
Author's final manuscript