Seminar talk, 21 February 2024

From Geometry of Differential Equations
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Speaker: Raffaele Vitolo

Title: Bi-Hamiltonian systems and projective geometry

We introduce the problem of classification of bi-Hamiltonian structures of KdV type under projective reciprocal transformations. This problem leads naturally to studying the compatibility of a first order localizable homogeneous Hamiltonian operator with a higher order homogeneous Hamiltonian operator. We study the simplest second-order and third-order case where the orbit contains a constant operator. Computations with weakly non local Hamiltonian operators have been made by techniques developed in a previous paper.

Joint work with P. Lorenzoni.

Slides: VitoloIUM2024.pdf