Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Prolongation Approach to B\"{a}cklund Transformation of
  Zhiber-Mikhailov-Shabat Equation   The prolongation structure of Zhiber-Mikhailov-Shabat (ZMS) equation is
studied by using Wahlquist-Estabrook's method. The Lax-pair for ZMS equation
and Riccati equations for pseudopotentials are formulated respectively from
linear and nonlinear realizations of the prolongation structure. Based on
nonlinear realization of the prolongation structure, an auto-B$\ddot{a}$cklund
transformation of ZMS equation is obtained.

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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: math