Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Miura transformations for Toda--type integrable systems, with
  applications to the problem of integrable discretizations   We study lattice Miura transformations for the Toda and Volterra lattices,
relativistic Toda and Volterra lattices, and their modifications. In
particular, we give three successive modifications for the Toda lattice, two
for the Volterra lattice and for the relativistic Toda lattice, and one for the
relativistic Volterra lattice. We discuss Poisson properties of the Miura
transformations, their permutability properties, and their role as localizing
changes of variables in the theory of integrable discretizations.

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The categories of this paper are: math
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol