Commutation relations of the transition matrix in the classical and quantum inverse scattering methods (local case)

In the classical inverse scattering method, an expression is derived for the Poisson brackets of the elements of the transition matrix in the local case when the Poisson brackets of the elements of the matrix of the auxiliary spectral problem contain in addition to the $\delta$ function a finite number of derivatives of it. An equation determining the classical $r$ matrix is obtained. The commutation relations for the elements of the quantum monodromy matrix in the analogous situation are discussed.