Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generic matrix superpotentials   A simple and algorithmic description of matrix shape invariant potentials is
presented. The complete lists of generic matrix superpotentials of dimension
$2\times2$ and of special superpotentials of dimension $3\times3$ are given
explicitly. In addition, a constructive description of superpotentials realized
by matrices of arbitrary dimension is presented. In this way an extended class
of integrable systems of coupled Schr\"odinger equation is classified. Examples
of such systems are considered in detail. New integrable multidimensional
models which are reduced to shape invariant systems via separation of variables
are presented also.

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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org