Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On integrability of Weingarten surfaces: a forgotten class   Rediscovered by a systematic search, a forgotten class of integrable surfaces
is shown to disprove the Finkel-Wu conjecture. The associated integrable
nonlinear partial differential equation $$ z_{yy} + (1/z)_{xx} + 2 = 0 $$
possesses a zero curvature representation, a third-order symmetry, and a
nonlocal transformation to the sine-Gordon equation $\phi_{\xi\eta} =
\sin\phi$. We leave open the problem of finding a Backlund autotransformation
and a recursion operator that would produce a local hierarchy.

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The categories of this paper are: patt-sol
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas