Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlocal symmetries related to B\"acklund transformation and their
  applications   Starting from nonlocal symmetries related to B\"acklund transformation (BT),
many interesting results can be obtained. Taking the well known potential KdV
(pKdV) equation as an example, a new type of nonlocal symmetry in elegant and
compact form which comes from BT is presented and used to make researches in
the following three subjects: two sets of negative pKdV hierarchies and their
corresponding bilinear forms are constructed; the nonlocal symmetry is
localized by introduction of suitable and simple auxiliary dependent variables
to generate new solutions from old ones and to consider some novel group
invariant solutions; some other models both in finite dimensions and infinite
dimensions are generated by comprising the original BT and evolution under new
nonlocal symmetry. The finite-dimensional models are completely integrable in
Liouville sense, which are shown equivalent to the results given through the
nonlinearization method for Lax pair.

27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin