Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Third-order superintegrable systems with potentials satisfying nonlinear
  equations   The conditions for superintegrable systems in two-dimensional Euclidean space
admitting separation of variables in an orthogonal coordinate system and a
functionally independent third-order integral are studied. It is shown that
only systems that separate in subgroup type coordinates, Cartesian or polar,
admit potentials that can be described in terms of nonlinear special functions.
Systems separating in parabolic or elliptic coordinated are shown to have
potentials with only non-movable singularities.

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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex