A hodograph transformation which applies to the heavenly equation

Details A hodograph transformation which applies to the heavenly equation A hodograph transformation which applies to the heavenly equation

2002-09-24

arxiv.org/abs/nlin/0209050v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

LaTeX2e with amsmath package, 11 pages

Scientific paper

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.

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