A Note on Weak ${\cal H}$-Spaces, Heavenly Equations and their Evolution Weak Heavenly Equations

J. F. Plebański; H. García-Compeán

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A Note on Weak ${\cal H}$-Spaces, Heavenly Equations and their Evolution Weak Heavenly Equations

J. F. Plebański·H. García-Compeán

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Abstract

\noindent It is find a non-linear partial differential equation which we show contains the first Heavenly equation of Self-dual gravity and generalize the second one. This differential equation we call "Weak Heavenly Equation" (${\cal WH}$-equation). For the two-dimensional case the ${\cal WH}$-equation is brought into the evolution form (Cauchy-Kovalevski form) using the Legendre transformation. Finally, we find that this transformed equation ("Evolution Weak Heavenly Equation") does admit very simple solutions.

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J. F. Plebański, H. García-Compeán. 1994-05-12. A Note on Weak ${\cal H}$-Spaces, Heavenly Equations and their Evolution Weak Heavenly Equations. https://arxiv.org/abs/hep-th/9405078

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