9 citations · 16 across the 6 of their papers we have counts for
7 papers
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…
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…
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…
Regular F -manifolds with eventual identities
Sara Perletti, Ian A. B. Strachan
Given an F-manifold one may construct a dual multiplication (generalizing the idea of an almost-dual Frobenius manifold introduced by Dubrovin) using a so-called eventual identity,…
Integrable systems, Nijenhuis geometry and Lauricella bi-flat structures
Paolo Lorenzoni, Sara Perletti
Combining the construction of integrable systems of hydrodynamic type starting from the Frölicher-Nijenhuis bicomplex associated with a (1,1)-tensor field with vanish…
Regular non-semisimple Dubrovin-Frobenius manifolds
Paolo Lorenzoni, Sara Perletti
We study regular non-semisimple Dubrovin-Frobenius manifolds in dimensions 2,3,4. We focus on the case where the Jordan canonical form of the operator of multiplication by the Eule…