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

Abstract

We develop a rigorous theory of non-local Hamiltonian 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 Hamiltonian structures.

55 pages

References in corpus (1)

• Rational matrix pseudodifferential operators

Cited by in corpus (6)

• Some algebraic properties of differential operators
• Rational matrix pseudodifferential operators
• Recursion Operators and Tri-Hamiltonian Structure of the First Heavenly Equation of Plebański
• Some remarks on non-commutative principal ideal rings
• Recursion operators and bi-Hamiltonian structure of the general heavenly equation
• A bi-Hamiltonian Integrable Two Component Generalization of the third-Order Burgers Equation