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 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.
Lorenzoni, P., Vitolo, R. (2023). Projective-geometric aspects of bi-Hamiltonian structures of KdV type. In Alexandre Vinogradov Memorial Conference on Diffieties, Cohomological Physics, and Other Animals, 2021 (pp.165-178). American Mathematical Society [10.1090/conm/788/15825].
Projective-geometric aspects of bi-Hamiltonian structures of KdV type
Lorenzoni, P;
2023
Abstract
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 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.
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