Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Real eigenvalues of a non-self-adjoint perturbation of the self-adjoint
  Zakharov-Shabat operator   We study the eigenvalues of the self-adjoint Zakharov-Shabat operator
corresponding to the defocusing nonlinear Schrodinger equation in the inverse
scattering method. Real eigenvalues exist when the square of the potential has
a simple well. We derive two types of quantization condition for the
eigenvalues by using the exact WKB method, and show that the eigenvalues stay
real for a sufficiently small non-self-adjoint perturbation when the potential
has some PT-like symmetry.

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The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
26
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: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg