5 papers
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 vari…
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 introdu…
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…