# Poisson vertex algebras in the theory of Hamiltonian equations

@article{Barakat2009PoissonVA, title={Poisson vertex algebras in the theory of Hamiltonian equations}, author={Ali Barakat and Alberto De Sole and Victor G. Kac}, journal={Japanese Journal of Mathematics}, year={2009}, volume={4}, pages={141-252} }

Abstract.We lay down the foundations of the theory of Poisson vertex algebras aimed at its applications to integrability of Hamiltonian partial differential equations. Such an equation is called integrable if it can be included in an infinite hierarchy of compatible Hamiltonian equations, which admit an infinite sequence of linearly independent integrals of motion in involution. The construction of a hierarchy and its integrals of motion is achieved by making use of the so called Lenard scheme…

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