A hodograph transformation which applies to the heavenly equation
  A 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. 
Manuel Manas and Luis Martinez Alonso