Bi-quantisation of stationary KdV hierarchy and Novikov's equations

In my talk I am going to make an introduction in the new approach to quantisation of dynamical systems. I will show that stationary KdV equations and Novikov's equations admit two compatible quantisations, i.e. two distinct commutation relations between the variables, such that a linear combination of the corresponding commutators is also a valid quantisation rule leading to the Heisenberg form of quantum equations. The picture is very similar to the bi-Hamiltonian structure in the case of classical integrable equations, when a linear combination of Poisson brackets is also a Poisson bracket.