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.