On third Poisson structure of KdV equation

The third Poisson structure of the KdV equation in terms of canonical free fields and the reduced WZNW model is discussed. We prove that it is diagonalized in the Lagrange variables which were used before in the formulation of 2d gravity. We propose a quantum path integral for the KdV equation based on this representation.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 103, No. 3, pp. 461–466, June, 1995.