Wahlquist-Estabrook method for the investigation of nonlinear evolution equations. Two-dimensional case

The Wahlquist-Estabrook method which yields the linear ''inverse scattering'' equations for a given system of the nonlinear evolution equations is considered. A short review is presented on the interpretation of prolongation forms as connection forms and also on a possible extension of the method for the case of two spatial dimensions. It is assumed that the second space variable enters the evolution equation in a special way so that the equation does not contains derivatives higher than the first one over this variable