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.
Non-local Poisson structures and applications to the theory of integrable systems / DE SOLE, Alberto; V. G., Kac. - In: JAPANESE JOURNAL OF MATHEMATICS. NEW SERIES. - ISSN 0289-2316. - STAMPA. - 8:2(2013), pp. 233-347. [10.1007/s11537-013-1306-z]
Non-local Poisson structures and applications to the theory of integrable systems
DE SOLE, ALBERTO;
2013
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
