  In this paper we describe the $\epsilon$-isothermic surfaces in the
pseudo-Euclidean 3-space and we obtain the pseudo-Calapso equation. In
sequence, we classify the Dupin surfaces in pseudo-Euclidean 3-space having
distinct principal curvatures and provide explicit coordinates for such
surfaces. As application of the theory, we give explicit solutions to the
pseudo-Calapso equation.
