The role of PreHamiltonian differential and difference operators in (classical) integrable systems

Sylvain Carpentier (Columbia University)

Tuesday 9th April 15:30-16:30 Maths 311B

Abstract

We discuss a relatively new algebraic structure in the theory of integrable

systems (of PDEs and differential-difference equations): the class of differential,

or difference, operators such that their image is a sub Lie algebra of the algebra

of evolutionary vector fields. These operators, called PreHamiltonian, encode most

attributes of integrability for a given system. We will explain how they provide

a natural non skew-symmetric generalization of the Hamiltonian (local and non-local)

formalism, and discuss what is their geometric nature.

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