Differential Geometry and Its Applications, Proc. Conf. Opava, Czechoslovakia, Aug. 24–28, 1992 (Silesian University, Opava, 1993) 103–122
Zero-curvature representations of partial differential equations are governed by "Maurer-Cartan equations," a set of quasilinear equations in total derivatives. To solve it one can use either the famous Wahlquist-Estabrook procedure, or to "fix the gauge" according to the procedure suggested in this paper. The computational example uses the equation uxy = f(u). It is also proved that for systems of differential equations in multidimension (more than two independent variables) no nontrivial zero-curvature representations exist unless the system is very overdetermined.