Bi-Hamiltonian systems from homogeneous operators, part 2

Abstract: I will present new results on the same topic on which I delivered a seminar on March 2026. More precisely, the topic is that of integrable systems defined by bi-Hamiltonian pairs of the following form: $A_1 = P_1 + R_k$ and $A_2 = P_2$, where $P_1$, $P_2$ are homogeneous first-order Hamiltonian operators and $R_k$ is a homogeneous Hamiltonian operator of degree (order) $k$. Many 'famous' integrable systems (KdV, AKNS, dispersive water waves etc.) are endowed with a bi-Hamiltonian pair of that form. We will illustrate recent advances on compatibility conditions and their geometric interpretation. The results will be published in arXiv soon.

See also arXiv:2602.14739, arXiv:2407.17189, arXiv:2311.13932.

Joint work with R. La Scala, X. Li, P. Lorenzoni, S. Opanasenko.

mathematical physicsanalysis of PDEsdifferential geometry

Audience: researchers in the topic

( slides | video )

Geometry of differential equations seminar