Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Partner symmetries and non-invariant solutions of four-dimensional
  heavenly equations   We extend our method of partner symmetries to the hyperbolic complex
Monge-Amp\`ere equation and the second heavenly equation of Pleba\~nski. We
show the existence of partner symmetries and derive the relations between them
for both equations. For certain simple choices of partner symmetries the
resulting differential constraints together with the original heavenly
equations are transformed to systems of linear equations by an appropriate
Legendre transformation. The solutions of these linear equations are
generically non-invariant. As a consequence we obtain explicitly new classes of
heavenly metrics without Killing vectors.

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The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: eess