On Equations Which Describe Pseudospherical Surfaces

Using the notion of a differential equation which describes an η ‐pseudospherical surface ( η ‐p.s.s.), we give a characterization of the equations of type u xt = F ( u , u x ,…, ∂ k u / ∂x k ), k ≥ 2, with this property. We obtain a systematic procedure to determine a linear problem for which a given equation is the integrability condition. The equations of type u xt = F ( u , u x ) were characterized by Rabelo and Tenenblat in another paper. The theory is applied to several equations, some of which were not known to describe η ‐p.s.s.