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

被引：0

作者：

Alberto De Sole

Victor G. Kac

机构：

[1] Università di Roma “La Sapienza”,Dipartimento di Matematica

[2] MIT.,Department of Mathematics

来源：

Japanese Journal of Mathematics | 2013年 / 8卷

关键词：

non-local Poisson vertex algebra; non-local Poisson structure; rational matrix pseudo-differential operators; Lenard–Magri scheme of integrability; bi-Hamiltonian integrable hierarchies; 37K10 (primary); 35Q53; 17B80; 17B69; 37K30; 17B63 (secondary);

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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.

引用

页码：233 / 347

页数：114

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