670 citations · 3.3k across the 47 of their papers we have counts for
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Double Poisson vertex algebras and non-commutative Hamiltonian equations
Alberto De Sole, Victor G. Kac, Daniele Valeri
We develop the formalism of double Poisson vertex algebras (local and non-local) aimed at the study of non-commutative Hamiltionan PDEs. This is a generalization of the theory of d…
On integrability of some bi-Hamiltonian two field systems of PDE
Alberto De Sole, Victor G. Kac, Refik Turhan
We continue the study of integrability of bi-Hamiltonian systems with a compatible pair of local Poisson structures (H_0,H_1), where H_0 is a strongly skew-adjoint operator. This i…
Structure of classical (finite and affine) W-algebras
Alberto De Sole, Victor G. Kac, Daniele Valeri
First, we derive an explicit formula for the Poisson bracket of the classical finite W-algebra W^{fin}(g,f), the algebra of polynomial functions on the Slodowy slice associated to…
Adler-Gelfand-Dickey approach to classical W-algebras within the theory of Poisson vertex algebras
Alberto De Sole, Victor G. Kac, Daniele Valeri
We put the Adler-Gelfand-Dickey approach to classical W-algebras in the framework of Poisson vertex algebras. We show how to recover the bi-Poisson structure of the KP hierarchy, t…
Integrability of Dirac reduced bi-Hamiltonian equations
Alberto De Sole, Victor G. Kac, Daniele Valeri
First, we give a brief review of the theory of the Lenard-Magri scheme for a non-local bi-Poisson structure and of the theory of Dirac reduction. These theories are used in the rem…