Local and non-local Poisson vertex algebras and applications to the theory of integrable systems (Lecture 2)

It is well known that the validity of the so called Lenard-Magri scheme of integrability of a bi-Hamiltonian PDE can be established if one has some precise information on the corresponding 1st variational Poisson cohomology for one of the two Hamiltonian operators. We will see how to compute the variational Poisson cohomology for any quasiconstant coefficient Hamiltonian operator with invertible leading coefficient.