3 citations · 3 across the 4 of their papers we have counts for
4 papers
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…
On the geometry of WDVV equations and their Hamiltonian formalism in arbitrary dimension
S. Opanasenko, R. Vitolo
It is known that in low dimensions WDVV equations can be rewritten as commuting quasilinear bi-Hamiltonian systems. We extend some of these results to arbitrary dimension and a…
Bi-Hamiltonian structures of WDVV-type
S. Opanasenko, R. Vitolo
We study a class of nonlinear PDEs that admit the same bi-Hamiltonian structure as WDVV equations: a Ferapontov-type first-order Hamiltonian operator and a homogeneous third-order…
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…