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Poisson vertex algebras and Hamiltonian PDE (2306.09709v2)
Published 16 Jun 2023 in math-ph, math.MP, math.RT, and nlin.SI
Abstract: We discuss the theory of Poisson vertex algebras and their generalizations in relation to integrability of Hamiltonian PDE. In particular, we discuss the theory of affine classical W-algebras and apply it to construct a large class of integrable Hamiltonian PDE. We also discuss non commutative Hamiltonian PDE in the framework of double PVA, and differential-difference Hamiltonian equations in the framework of multiplicative PVA.
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