6 citations · 14 across the 10 of their papers we have counts for
8 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…
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…
Integrable hierarchies and F-manifolds with compatible connection
Paolo Lorenzoni, Sara Perletti, Karoline van Gemst
Building on the interplay between geometry and integrability, we show that F-manifolds with compatible connection are the geometric counterpart of integrable sys…
Bi-Hamiltonian structures of KdV type, cyclic Frobenius algebrae and Monge metrics
P. Lorenzoni, R. Vitolo
We study algebraic and projective geometric properties of Hamiltonian trios determined by a constant coefficient second-order operator and two first-order localizable operators of…
Weakly nonlocal Poisson brackets, Schouten brackets and supermanifolds
P. Lorenzoni, R. Vitolo
Poisson brackets between conserved quantities are a fundamental tool in the theory of integrable systems. The subclass of weakly nonlocal Poisson brackets occurs in many significan…
Bi-Hamiltonian structures of KdV type
P. Lorenzoni, A. Savoldi, R. Vitolo
Combining an old idea of Olver and Rosenau with the classification of second and third order homogeneous Hamiltonian operators we classify compatible trios of two-component homogen…