Poisson vertex algebras and Hamiltonian PDE

2023/06/16 by De Sole, Alberto, Kac, Victor G., Valeri, Daniele
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2306.09709

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.

Related

• Introduction to vertex algebras, Poisson vertex algebras, and integrable Hamiltonian PDE
• Adler-Oevel-Ragnisco type operators and Poisson vertex algebras
• Poisson integrators
• Poisson structure and Integrability of a Hamiltonian flow for the inhomogeneous six-vertex model
• Multidimensional multiplicative Poisson vertex algebras