Abstract: | In is known that the equations [ut ? g(u)ux]x = ±g′(u) describe pseudo-spherical surfaces, i.e. that these equations are the integrability conditions for the structural equations of such surfaces, provided g satisfies g′ + µg = θ. In this paper we obtain self-Bäcklund transformations for these equations by a geometric method, and show how the inverse scattering method generates global solutions. |