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SUMMARY:Raffaele Vitolo (Università del Salento)
DTSTART:20260318T162000Z
DTEND:20260318T180000Z
DTSTAMP:20260423T023008Z
UID:GDEq/153
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GDEq/153/">B
 i-Hamiltonian systems from homogeneous operators</a>\nby Raffaele Vitolo (
 Università del Salento) as part of Geometry of differential equations sem
 inar\n\n\nAbstract\nMany "famous" integrable systems (KdV\, AKNS\, dispers
 ive water waves etc.) have a bi-Hamiltonian pair of the following form: $A
 _1 = P_1 + R_k$ and $A_2 = P_2$\, where $P_1$\, $P_2$ are homogeneous firs
 t-order Hamiltonian operators and $R_k$ is a homogeneous Hamiltonian opera
 tor of degree (order) $k$. The Hamiltonian property of $P_1$\, $P_2$ and t
 heir compatibility were given an explicit analytic form and geometric inte
 rpretation long ago (Dubrovin\, Novikov\, Ferapontov\, Mokhov). The Hamilt
 onian property of $R_k$ was studied in the past (Doyle\, Potemin\; $k=2\,3
 $) and recently revisited with interesting results.\n\nIn this talk\, we i
 llustrate the analytic form and some preliminary geometric interpretation 
 of the compatibility conditions between $P_i$ and $R_k$\, $k=2\,3$.\n\nSee
  the recent papers <a href="https://arxiv.org/abs/2602.14739">arXiv:2602.1
 4739</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\nJoi
 nt work with P. Lorenzoni and S. Opanasenko.\n
LOCATION:https://researchseminars.org/talk/GDEq/153/
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