4 papers · 1 filter
Multi-component Hamiltonian difference operators
Matteo Casati, Daniele Valeri
In this paper we study local Hamiltonian operators for multi-component evolutionary differential-difference equations. We address two main problems: the first one is the classifica…
Three computational approaches to weakly nonlocal Poisson brackets
M. Casati, P. Lorenzoni, R. Vitolo
We compare three different ways of checking the Jacobi identity for weakly nonlocal Poisson brackets using the theory of distributions, of pseudodifferential operators and of Poiss…
A Darboux-Getzler theorem for scalar difference Hamiltonian operators
Matteo Casati, Jing Ping Wang
In this paper we extend to the difference case the notion of Poisson-Lichnerowicz cohomology, an object encapsulating the building blocks for the theory of deformations of Hamilton…
On a class of third-order nonlocal Hamiltonian operators
M. Casati, E. V. Ferapontov, M. V. Pavlov +1
Based on the theory of Poisson vertex algebras we calculate skew-symmetry conditions and Jacobi identities for a class of third-order nonlocal operators of differential-geometric t…