2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143636We establish a correspondence between Darboux's special isothermic surfaces of type (A,0,C,D) and the solutions of the second order PDE : uΔ(u)-|\nabla(u)|^{2}+Φ^{4}=s, s \in R. We then use the classical Darboux transformation for isothermic surfaces to construct a Bäcklund transformation for this equation and prove a superposition formula for its solutions. As an application we discuss 1 and 2-soliton solutions and the corresponding surfaces.18 pages, 5 figures, to appear in the AMS Contemporary Mathematics Series, "Proceedings of the Congress in memory of Alfred Gray" (eds. M. Fernandez, J.A. Wolf)Differential Geometry53A30, 53A05text