Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Massive ODE/IM Correspondence and Non-linear Integral Equations for
  $A_r^{(1)}$-type modified Affine Toda Field Equations   The massive ODE/IM correspondence is a relation between the linear problem
associated with modified affine Toda field equations and two-dimensional
massive integrable models. We study the massive ODE/IM correspondence for the
$A_r^{(1)}$-type modified affine Toda field equations. Based on the
$\psi$-system satisfied by the solutions of the linear problem, we derive the
Bethe ansatz equations and determine the asymptotic behavior of the Q-functions
for large value of the spectral parameter. We derive the non-linear integral
equations for the Q-functions from the Bethe ansatz equations. We compute the
effective central charge in the UV limit, which is identified with the one of
the non-unitary $WA_r$ minimal models when the solution has trivial monodromy
around the origin of the complex plane.

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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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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: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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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: comp-gas