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math-ph2026
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…
nlin.SI2026
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…