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arXiv · 1412.7376

Doubrov-Ferapontov general heavenly equation and the hyper-K\"ahler hierarchy

L. V. Bogdanov
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Abstract

We give a description of recently introduced Doubrov-Ferapontov general heavenly equation in terms of closed differential Pl\"ucker two-form, rationally depending on the spectral parameter. We demonstrate that general heavenly equation is an important generating equation in the context of Takasaki hyper-K\"ahler hierarchy, and it is also directly connected to hyper-K\"ahler geometry through the Gindikin construction. We develop a $\bar{\partial}$-dressing scheme and introduce a formula for the potential satisfying the general heavenly equation. Multidimensional generalization is also outlined.

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L. V. Bogdanov. 2014-12-23. Doubrov-Ferapontov general heavenly equation and the hyper-K\"ahler hierarchy. https://arxiv.org/abs/1412.7376

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