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

TL;DR

This paper advances the Lenard-Magri scheme for compatible non-local Poisson structures, demonstrating its effectiveness in establishing integrability of various evolution and hyperbolic equations, some of which may be novel.

Contribution

It extends the theory of non-local Poisson structures and applies the scheme to prove integrability of new and existing equations in the field.

Findings

Proved integrability of several evolution equations.

Established integrability of certain hyperbolic equations.

Identified some potentially new integrable equations.

Abstract

We develop further the Lenard-Magri scheme of integrability for a pair of compatible non-local Poisson structures, which we discussed in Part I. We apply this scheme to several such pairs, proving thereby integrability of various evolution equations, as well as hyperbolic equations. Some of these equations may be new.