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

作者：De Sole Alberto^*; Kac Victor G

来源：Japanese Journal of Mathematics, 2013, 8(2): 233-347.

DOI：10.1007/s11537-013-1306-z

• non-local Poisson vertex algebra
• non-local Poisson structure
• rational matrix pseudo-differential operators
• Lenard-Magri scheme of integrability
• bi-Hamiltonian integrable hierarchies

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.

• 出版日期2013-9