Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Einstein--Weyl spaces and dispersionless Kadomtsev--Petviashvili
  equation from Painlev\'e I and II   We present two constructions of new solutions to the dispersionless KP (dKP)
equation arising from the first two Painlev\'e transcendents. The first
construction is a hodograph transformation based on Einstein--Weyl geometry,
the generalised Nahm's equation and the isomonodromy problem. The second
construction, motivated by the first, is a direct characterisation of solutions
to dKP which are constant on a central quadric.
  We show how the solutions to the dKP equations can be used to construct some
three-dimensional Einstein--Weyl structures, and four--dimensional
anti-self-dual null-K\"ahler metrics.

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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
37
The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: quant-ph