Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrable chains on algebraic curves   The discrete Lax operators with the spectral parameter on an algebraic curve
are defined. A hierarchy of commuting flows on the space of such operators is
constructed. It is shown that these flows are linearized by the spectral
transform and can be explicitly solved in terms of the theta-functions of the
spectral curves. The Hamiltonian theory of the corresponding systems is
analyzed. The new type of completely integrable Hamiltonian systems associated
with the space of rank $r=2$ discrete Lax operators on a {\it variable} base
curve is found.

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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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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: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg