3 papers
nlin.SI2026
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…
nlin.SI2025
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…
nlin.SI2024
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…