5 papers
Duality of Hamiltonian and Lagrangian formulations for integrable systems
Pierandrea Vergallo, Mats Vermeeren
We introduce the concept of Hamiltonian potential variables to map Hamiltonian operators into symplectic operators in a dual space. This generalises the classical trick of switchin…
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…
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…
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…
Line geometry of pairs of second-order Hamiltonian operators and quasilinear systems
Giorgio Gubbiotti, Bert van Geemen, Pierandrea Vergallo
We demonstrate that a pair consisting of a second-order homogeneous Hamiltonian structure in components and its associated system of conservation laws is in bijective correspon…