Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lax pairs, Painlev\'e properties and exact solutions of the alogero
  Korteweg-de Vries equation and a new (2+1)-dimensional equation   We prove the existence of a Lax pair for the Calogero Korteweg-de Vries
(CKdV) equation. Moreover, we modify the T operator in the the Lax pair of the
CKdV equation, in the search of a (2+1)-dimensional case and thereby propose a
new equation in (2+1) dimensions. We named this the (2+1)-dimensional CKdV
equation. We show that the CKdV equation as well as the (2+1)-dimensional CKdV
equation are integrable in the sense that they possess the Painlev\'e property.
Some exact solutions are also constructed.

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The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg