15 citations · 103 across the 17 of their papers we have counts for
17 papers
Multidimensional multiplicative Poisson vertex algebras
Pengfei Yang, Matteo Casati
In this paper we introduce the notion of multidimensional multiplicative Poisson vertex algebra, the generalization of the notion of multiplicative Poisson vertex algebra to a diff…
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 ,…
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…
Multidimensional Nonhomogeneous Quasi-Linear Systems and Their Hamiltonian Structure
Xin Hu, Matteo Casati
In this paper, we investigate multidimensional first-order quasi-linear systems and find necessary conditions for them to admit Hamiltonian formulation. The insufficiency of the co…
Multidimensional Integrable Deformations of Integrable PDEs
Matteo Casati, Danda Zhang
In a recent series of papers by Lou et al., it was conjectured that higher dimensional integrable equations may be constructed by utilizing some conservation laws of (1 + 1)-dimens…
Weakly nonlocal Poisson brackets: tools, examples, computations
Matteo Casati, Paolo Lorenzoni, Daniele Valeri +1
We implement an algorithm for the computation of Schouten bracket of weakly nonlocal Hamiltonian operators in three different computer algebra systems: Maple, Reduce and Mathematic…
Hamiltonian structures for integrable nonabelian difference equations
Matteo Casati, Jing Ping Wang
In this paper we extensively study the notion of Hamiltonian structure for nonabelian differential-difference systems, exploring the link between the different algebraic (in terms…
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…
Normal forms of dispersive scalar Poisson brackets with two independent variables
Guido Carlet, Matteo Casati, Sergey Shadrin
We classify the dispersive Poisson brackets with one dependent variable and two independent variables, with leading order of hydrodynamic type, up to Miura transformations. We show…
MasterPVA and WAlg: Mathematica packages for Poisson vertex algebras and classical affine -algebras
Matteo Casati, Daniele Valeri
We give an introduction to the Mathematica packages "MasterPVA" and "MasterPVAmulti used to compute lambda-brackets in Poisson vertex algebras, which play an important role in the…
Poisson cohomology of scalar multidimensional Dubrovin-Novikov brackets
Guido Carlet, Matteo Casati, Sergey Shadrin
We compute the Poisson cohomology of a scalar Poisson bracket of Dubrovin-Novikov type with independent variables. We find that the second and third cohomology groups are gener…
Dispersive deformations of the Hamiltonian structure of Euler's equations
Matteo Casati
Euler's equations for a two-dimensional system can be written in Hamiltonian form, where the Poisson bracket is the Lie-Poisson bracket associated to the Lie algebra of divergence…
On deformations of multidimensional Poisson brackets of hydrodynamic type
Matteo Casati
The theory of Poisson Vertex Algebras (PVAs) is a good framework to treat Hamiltonian partial differential equations. A PVA consists of a pair of a…