Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and
  Kac-van Moerbeke Hierarchies   Combining algebro-geometric methods and factorization techniques for finite
difference expressions we provide a complete and self-contained treatment of
all real-valued quasi-periodic finite-gap solutions of both the Toda and
Kac-van Moerbeke hierarchies. In order to obtain our principal new result, the
algebro-geometric finite-gap solutions of the Kac-van Moerbeke hierarchy, we
employ particular commutation methods in connection with Miura-type
transformations which enable us to transfer whole classes of solutions (such as
finite-gap solutions) from the Toda hierarchy to its modified counterpart, the
Kac-van Moerbeke hierarchy, and vice versa.

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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: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom