Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Painlev\'e property, local and nonlocal symmetries and symmetry
  reductions for a (2+1)-dimensional integrable KdV equation   The Painlev\'e property for a (2+1)-dimensional Korteweg-de Vries (KdV)
extension, the combined KP3 (Kadomtsev- Petviashvili) and KP4 (cKP3-4) is
proved by using Kruskal's simplification. The truncated Painlev\'e expansion is
used to find the Schwartz form, the B\"acklund/Levi transformations and the
residual nonlocal symmetry. The residual symmetry is localized to find its
finite B\"acklund transformation. The local point symmetries of the model
constitute a centerless Kac-Moody-Virasoro algebra. The local point symmetries
are used to find the related group invariant reductions including a new Lax
integrable model with a fourth order spectral problem. The finite
transformation theorem or the Lie point symmetry group is obtained by using a
direct method.

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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph