Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On two aspects of the Painleve analysis   We use the Calogero equation to illustrate the following two aspects of the
Painleve analysis of nonlinear PDEs. First, if a nonlinear equation passes the
Painleve test for integrability, the singular expansions of its solutions
around characteristic hypersurfaces can be neither single-valued functions of
independent variables nor single-valued functionals of data. Second, if the
truncation of singular expansions of solutions is consistent, the truncation
not necessarily leads to the simplest, or elementary, auto-Backlund
transformation related to the Lax pair.

30
The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs