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A hodograph transformation which applies to the heavenly equation

Manuel Manas·Luis Martinez Alonso
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Abstract

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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Manuel Manas, Luis Martinez Alonso. 2002-09-24. A hodograph transformation which applies to the heavenly equation. https://arxiv.org/abs/nlin/0209050

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