Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometry of B\"acklund Transformations I: Generality   Using Cartan's Method of Equivalence, we prove an upper bound for the
generality of generic rank-1 B\"acklund transformations relating two hyperbolic
Monge-Amp\`ere systems. In cases when the B\"acklund transformation admits a
symmetry group whose orbits have codimension 1, 2, or 3, we obtain
classification results and new examples of auto-B\"acklund transformations.

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The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th