Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Doubrov-Ferapontov general heavenly equation and the hyper-K\"ahler
  hierarchy   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.

26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci