6 citations · 14 across the 10 of their papers we have counts for
4 papers · 1 filter
Cyclic F-manifolds, distinguished connections and integrability
Alessandro Arsie, Paolo Lorenzoni
We show that the geometry of Hertling-Manin F-manifolds provide the appropriate theoretical framework for studying the integrability of quasilinear systems of first-o…
Gibbons-Tsarev type systems and Eventual identities
Alessandro Arsie, Paolo Lorenzoni, Sara Perletti +1
We show that non-diagonalisable reductions of the dKP equation associated with regular non-semisimple -manifolds cannot exist. The proof is based on the derivation and study of…
Generalised (bi-)Hamiltonian structures of hydrodynamic type and (bi-)flat F-manifolds
Paolo Lorenzoni, Zhe Wang
We introduce the notions of generalised (bi-)Hamiltonian structures which generalise naturally the (bi-)Hamiltonian structures of evolutionary partial differential equations. In th…
Compatible pairs of Hamiltonian operators of the first and third orders
Paolo Lorenzoni, Stanislav Opanasenko, Raffaele Vitolo
We compute general compatibility conditions between a weakly nonlocal homogeneous Hamiltonian operator and a third-order homogeneous Hamiltonian operator. Such operators determine…