10 citations · 40 across the 15 of their papers we have counts for
18 papers
Discrete differential-geometric Poisson brackets: general theory and explicit constructions
Marta Dell'Atti, Giorgio Gubbiotti, Pierandrea Vergallo
We review the discrete theory of differential-geometric Poisson brackets as introduced by B. A. Dubrovin, and we present a complete proof of their characterisation in the non-degen…
Classification of pairs of second-order Hamiltonian operators and hydrodynamic type systems in six components
Giorgio Gubbiotti, Lambertus Van Geemen, Pierandrea Vergallo
Following a recent characterisation of hydrodynamic systems with second-order Hamiltonian structure in terms of alternating three-forms on the projective space, we present a comple…
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…
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…
Quasilinear differential constraints for parabolic systems of Jordan-block type
Alessandra Rizzo, Pierandrea Vergallo
We prove that linear degeneracy is a necessary conditions for systems in Jordan-block form to admit a compatible quasilinear differential constraint. Such condition is also suffici…
Hamiltonian aspects of the kinetic equation for soliton gas
Pierandrea Vergallo, Evgeny V. Ferapontov
We investigate Hamiltonian aspects of the integro-differential kinetic equation for dense soliton gas which results as a thermodynamic limit of the Whitham equations. Under a delta…
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…
Domain-wall orientation in antiferromagnets controlled by magnetoelastic effects
Pierandrea Vergallo, Bennet Karetta, Giancarlo Consolo +1
In this paper, we develop the mathematical framework to describe the physical phenomenon behind the equilibrium configuration joining two antiferromagnetic domains. We firstly defi…
Non-homogeneous Hamiltonian structures for quasilinear systems
Pierandrea Vergallo
This paper aims at investigating necessary (and sufficient) conditions for quasilinear systems of first order PDEs to be Hamiltonian, with non-homogeneous operators of order 1 + 0,…
Solutions to the wave equation for commuting flows of dispersionless PDEs
Natale Manganaro, Alessandra Rizzo, Pierandrea Vergallo
Motivated by the viewpoint of integrable systems, we study commuting flows of 2-component quasilinear equations, reducing to investigate the solutions of the wave equation with non…
Hamiltonian systems of Jordan block type: delta-functional reductions of the kinetic equation for soliton gas
Pierandrea Vergallo, Evgeny V. Ferapontov
We demonstrate that linear degeneracy is a necessary condition for quasilinear systems of Jordan block type to possess first-order Hamiltonian structures. Multi-Hamiltonian formula…
Classification of degenerate non-homogeneous Hamiltonian operators
Marta Dell'Atti, Pierandrea Vergallo
In this paper, the authors investigate non-homogeneous Hamiltonian operators composed of a first-order Dubrovin-Novikov operator and an ultralocal one. The study of such operators…
Quasilinear systems of first order PDEs with nonlocal Hamiltonian structures
Pierandrea Vergallo
In this paper we wonder whether a quasilinear system of PDEs of first order admits Hamiltonian formulation with local and nonlocal operators. By using the theory of differential co…
Projective geometry of homogeneous second order Hamiltonian operators
Pierandrea Vergallo, Raffaele Vitolo
We prove the invariance of homogeneous second-order Hamiltonian operators under the action of projective reciprocal transformations. We establish a correspondence between such oper…
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…
Homogeneous Hamiltonian operators and the theory of coverings
Pierandrea Vergallo, Raffaele Vitolo
A new method (by Kersten, Krasil'shchik and Verbovetsky), based on the theory of differential coverings, allows to relate a system of PDEs with a differential operator in such a wa…