Bäcklund Transformations and Inverse Scattering Solutions for Some Pseudospherical Surface Equations

In is known that the equations u_t ? g(u)u_x]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.