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SUMMARY:Raffaele Vitolo (Università del Salento)
DTSTART:20261021T162000Z
DTEND:20261021T180000Z
DTSTAMP:20261025T075955Z
UID:GDEq/161
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GDEq/161/">B
 i-Hamiltonian systems from homogeneous operators\, part 2</a>\nby Raffaele
  Vitolo (Università del Salento) as part of Geometry of differential equa
 tions seminar\n\n\nAbstract\nI will present new results on the same topic 
 on which I delivered a seminar on March 2026. More precisely\, the topic i
 s that of integrable systems defined by bi-Hamiltonian pairs of the follow
 ing form: $A_1 = P_1 + R_k$ and $A_2 = P_2$\, where $P_1$\, $P_2$ are homo
 geneous first-order Hamiltonian operators and $R_k$ is a homogeneous Hamil
 tonian operator of degree (order) $k$. Many 'famous' integrable systems (K
 dV\, AKNS\, dispersive water waves etc.) are endowed with a bi-Hamiltonian
  pair of that form. We will illustrate recent advances on compatibility co
 nditions and their geometric interpretation. The results will be published
  in arXiv soon.\n\nSee also <a href="https://arxiv.org/abs/2602.14739">arX
 iv:2602.14739</a>\, <a href="https://arxiv.org/abs/2407.17189">arXiv:2407.
 17189</a>\, <a href="https://arxiv.org/abs/2311.13932">arXiv:2311.13932</a
 >.\n\nJoint work with R. La Scala\, X. Li\, P. Lorenzoni\, S. Opanasenko.\
 n
LOCATION:https://researchseminars.org/talk/GDEq/161/
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