2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/80322A hodograph transformation for a wide family of multidimensional nonlinear partial differential equations is presented. It is used to derive solutions of the heavenly equation (dispersionless Toda equation) as well as a family of explicit ultra-hyperbolic selfdual vacuum spaces admiting only one Killing vector which is not selfdual, we also give the corresponding explicit Einstein--Weyl structures.LaTeX2e with amsmath package, 11 pagesExactly Solvable and Integrable Systemstext