Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gauge Symmetry Origin of B\"acklund Transformations for Painlev\'e
  Equations   We identify the self-similarity limit of the second flow of $sl(N)$ mKdV
hierarchy with the periodic dressing chain thus establishing % a connection to
$A^{(1)}_{N-1}$ invariant
  Painlev\'e equations. The $A^{(1)}_{N-1}$ B\"acklund symmetries of dressing
equations and Painlev\'e equations are obtained in the self-similarity limit of
gauge transformations of the mKdV hierarchy realized as zero-curvature
equations on the loop algebra $\widehat{sl}(N)$ endowed with a principal
gradation.

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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
3
The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga