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math.DG2025
On the structure of homogeneous local Poisson brackets
Guido Carlet, Matteo Casati
We consider an arbitrary Dubrovin-Novikov bracket of degree , namely a homogeneous degree local Poisson bracket on the loop space of a smooth manifold of dimension ,…
math.DG2017
Higher order dispersive deformations of multidimensional Poisson brackets of hydrodynamic type
Matteo Casati
The theory of multidimensional Poisson vertex algebras (mPVAs) provides a completely algebraic formalism to study the Hamiltonian structure of PDEs, for any number of dependent and…