Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Miura Transformations and Volterra-Type Equations Associated with the
  Adler-Bobenko-Suris Equations   We construct Miura transformations mapping the scalar spectral problems of
the integrable lattice equations belonging to the Adler-Bobenko-Suris (ABS)
list into the discrete Schr\"odinger spectral problem associated with
Volterra-type equations. We show that the ABS equations correspond to
B\"acklund transformations for some particular cases of the discrete
Krichever-Novikov equation found by Yamilov (YdKN equation). This enables us to
construct new generalized symmetries for the ABS equations. The same can be
said about the generalizations of the ABS equations introduced by Tongas,
Tsoubelis and Xenitidis. All of them generate B\"acklund transformations for
the YdKN equation. The higher order generalized symmetries we construct in the
present paper confirm their integrability.

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The categories of this paper are: hep-lat
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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: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: atom-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: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg