Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dirichlet and Neumann Problems for String Equation, Poncelet Problem and
  Pell-Abel Equation   We consider conditions for uniqueness of the solution of the Dirichlet or the
Neumann problem for 2-dimensional wave equation inside of bi-quadratic
algebraic curve. We show that the solution is non-trivial if and only if
corresponding Poncelet problem for two conics associated with the curve has
periodic trajectory and if and only if corresponding Pell-Abel equation has a
solution.

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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con