4 papers · 1 filter
Geometric aspects of non-homogeneous 1+0 operators
Marta Dell'Atti, Alessandra Rizzo, Pierandrea Vergallo
Led by the key example of the Korteweg-de Vries equation, we study pairs of Hamiltonian operators which are non-homogeneous and are given by the sum of a first-order operator and a…
Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators
Giorgio Gubbiotti, Francesco Oliveri, Emanuele Sgroi +1
We study from an algebraic and geometric viewpoint Hamiltonian operators which are sum of a non-degenerate first-order homogeneous operator and a Poisson tensor. In flat coordinate…
Nonlocal Hamiltonian structures of the kinetic equation for soliton gas under polychromatic reductions
Pierandrea Vergallo
We deepen the existence of a nonlocal Hamiltonian formalism for the El's kinetic equation for soliton gas under the polychromatic reduction for a class of interaction kernels. The…
Classification of bi-Hamiltonian pairs extended by isometries
Maxim V. Pavlov, Pierandrea Vergallo, Raffaele Vitolo
The aim of this article is to classify pairs of first-order Hamiltonian operators of Dubrovin-Novikov type such that one of them has a non-local part defined by an isometry of its…