The theory of triples of Poisson brackets and related integrable systems, based on a classical R-matrix R ∈ EndF (g), where g is a finite dimensional associative algebra over a field F viewed as a Lie algebra, was developed by Oevel-Ragnisco and Li-Parmentier [OR89, LP89]. In the present paper we develop an “affine” analogue of this theory by introducing the notion of a continuous Poisson vertex algebra and constructing triples of Poisson λ-brackets. We introduce the corresponding Adler type identities and apply them to integrability of hierarchies of Hamiltonian PDEs.
Adler–Oevel-Ragnisco type operators and Poisson vertex algebras / De Sole, Alberto; Kac, Victor G.; Valeri, Daniele. - In: PURE AND APPLIED MATHEMATICS QUARTERLY. - ISSN 1558-8599. - 20:3(2024), pp. 1181-1249. [10.4310/pamq.2024.v20.n3.a5]
Adler–Oevel-Ragnisco type operators and Poisson vertex algebras
De Sole, Alberto;Valeri, Daniele
2024
Abstract
The theory of triples of Poisson brackets and related integrable systems, based on a classical R-matrix R ∈ EndF (g), where g is a finite dimensional associative algebra over a field F viewed as a Lie algebra, was developed by Oevel-Ragnisco and Li-Parmentier [OR89, LP89]. In the present paper we develop an “affine” analogue of this theory by introducing the notion of a continuous Poisson vertex algebra and constructing triples of Poisson λ-brackets. We introduce the corresponding Adler type identities and apply them to integrability of hierarchies of Hamiltonian PDEs.File | Dimensione | Formato | |
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