5 papers
Recursion and Hamiltonian operators for integrable nonabelian difference equations
Matteo Casati, Jing Ping Wang
In this paper, we carry out the algebraic study of integrable differential-difference equations whose field variables take values in an associative (but not commutative) algebra. W…
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…
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…