Аннотация:
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.
