Symplectic operators and Lagrangian multiforms for bi-Hamiltonian systems

Mats Vermeeren (Loughborough University)

Tuesday 6th October 16:00-17:00
Maths 311B

Abstract

This talk presents some recent insights into the Lagrangian structure of bi-Hamiltonian systems. It is well- known that for many integrable Hamiltonian PDEs (e.g. KdV equation), passing to a potential variable allows one to formulate a variational principle. We show that such a potential variable is fundamentally connected to the Hamiltonian operator. The transformation to potential variables turns a compatible pair of Hamiltonian operators into a compatible pair of symplectic operators. Each of these symplectic operators can be used to construct a Lagrangian multiform - a structure that describes an integrable hierarchy in a single variational principle.

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