Doubrov-Ferapontov general heavenly equation and the hyper-Kähler hierarchy
Abstract
We give a description of a recently introduced Doubrov-Ferapontov general heavenly equation in terms of a closed differential Plücker two-form, rationally depending on the spectral parameter. We demonstrate that the general heavenly equation is an important generating equation in the context of Takasaki hyper-Kähler hierarchy, and it is also directly connected to hyper-Kähler geometry through the Gindikin construction. We develop a \bar{\partial }-dressing scheme and introduce a formula for the potential satisfying of the general heavenly equation. Multidimensional generalization is also outlined.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- June 2015
- DOI:
- 10.1088/1751-8113/48/23/235202
- Bibcode:
- 2015JPhA...48w5202B