ON DIFFERENTIAL-EQUATIONS DESCRIBING PSEUDO-SPHERICAL SURFACES

We give a complete classification of the evolution equations partial d erivative u/partial derivative t=F(u, partial derivative u/partial der ivative x,..., partial derivative(k)u/partial derivative x(k)) which d escribe pseudo-spherical surfaces, without any a priori assumptions on the presence of a spectral parameter. We also prove a local existence theorem to the effect that given two differential equations describin g pseudo-spherical surfaces (not necessarily evolutionary), there exis ts, under a technical assumption, a smooth mapping transforming any su itably generic solution of one equation into a solution of the other. (C) 1995 Academic Press, Inc.