8 citations · 23 across the 7 of their papers we have counts for
10 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…
Matrix Dressing Beyond Pfaff-Toda
Sylvain Carpentier, Marta Dell'Atti
We develop a matrix pseudodifference operator framework that places theAdler-Pfaff and Pfaff-Toda hierarchies in a common algebraic setting. The bi-infinite Adler-Pfaff hierarchy t…
r-Matrices for integrable systems
Marta Dell'Atti
We consider some algebraic and geometric aspects of the theory of integrable systems in finite dimensions, associated with the existence of a classical -matrix, first introduced…
Random matrix ensembles and integrable differential identities
Costanza Benassi, Marta Dell'Atti, Antonio Moro
Integrable differential identities, together with ensemble-specific initial conditions, provide an effective approach for the characterisation of relevant observables and state fun…
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…
Spaces of initial conditions for quartic Hamiltonian systems of Painlevé and quasi-Painlevé type
Marta Dell'Atti, Thomas Kecker
The geometric approach for Painlevé and quasi-Painlevé differential equations in the complex plane is applied to non-autonomous Hamiltonian systems, quartic in the dependent variab…
Geometric approach for the identification of Hamiltonian systems of quasi-Painlevé type
Marta Dell'Atti, Thomas Kecker
Some new Hamiltonian systems of quasi-Painlevé type are presented and the analogue of Okamoto's space of initial conditions computed. Using the geometric approach that was introduc…
Lagrangian multiforms on coadjoint orbits for finite-dimensional integrable systems
Vincent Caudrelier, Marta Dell'Atti, Anup Anand Singh
Lagrangian multiforms provide a variational framework to describe integrable hierarchies. The case of Lagrangian -forms covers finite-dimensional integrable systems. We use the…
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…
Symmetric Matrix Ensemble and Integrable Hydrodynamic Chains
Costanza Benassi, Marta Dell'Atti, Antonio Moro
The partition function of the Symmetric Matrix Ensemble is identified with the function of a particular solution of the Pfaff Lattice. We show that in the case of even power in…