6 papers
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…
Hamiltonian formalism for non-diagonalisable systems of hydrodynamic type
Paolo Lorenzoni, Sara Perletti, Karoline van Gemst
We study the system of first order PDEs for pseudo-Riemannian metrics governing the Hamiltonian formalism for systems of hydrodynamic type. In the diagonal setting the integrabilit…
The generalised hodograph method for non-diagonalisable integrable systems of hydrodynamic type
Paolo Lorenzoni, Sara Perletti, Karoline van Gemst
We extend the generalised hodograph method to regular non- diagonalisable integrable systems of hydrodynamic type, in light of the relation between such systems and F-manifolds wit…