9 citations · 9 across the 3 of their papers we have counts for
5 papers
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…
Deformations of non semisimple Poisson pencils of hydrodynamic type
Alberto Della Vedova, Paolo Lorenzoni, Andrea Savoldi
We study deformations of two-component non semisimple Poisson pencils of hydrodynamic type associated with Balinski\vı-Novikov algebras. We show that in most cases the second order…
Degenerate first-order Hamiltonian operators of hydrodynamic type in 2D
Andrea Savoldi
First-order Hamiltonian operators of hydrodynamic type were introduced by Drubrovin and Novikov in 1983. In 2D, they are generated by a pair of contravariant metrics , $\tilde{g…
On deformations of one-dimensional Poisson structures of hydrodynamic type with degenerate metric
Andrea Savoldi
We provide a complete list of two- and three-component Poisson structures of hydrodynamic type with degenerate metric, and study their homogeneous deformations. In the non-degenera…
Hamiltonian operators of Dubrovin-Novikov type in 2D
E. V. Ferapontov, P. Lorenzoni, A. Savoldi
First order Hamiltonian operators of differential-geometric type were introduced by Dubrovin and Novikov in 1983, and thoroughly investigated by Mokhov. In 2D, they are generated b…