Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On integrals of the tronqu\'{e}e solutions and the associated
  Hamiltonians for the Painlev\'{e} II equation   We consider a family of tronqu\'{e}e solutions of the Painelv\'{e} II
equation \begin{equation*} q''(s)=2q(s)^3+sq(s)-(2\alpha+\frac12), \qquad
\alpha > -\frac12, \end{equation*} which is characterized by the Stokes
multipliers $$s_1=-e^{-2\alpha \pi i },\quad s_2=\omega, \quad s_3=-e^{2 \alpha
\pi i} $$ with $\omega$ being a free parameter. These solutions include the
well-known generalized Hastings-McLeod solution as a special case if
$\omega=0$. We derive asymptotics of integrals of the tronqu\'{e}e solutions
and the associated Hamiltonians over the real axis for $\alpha > -1/2$ and
$\omega \geq 0$, with the constant terms evaluated explicitly. Our results
agree with those already known in the literature if the parameters $\alpha$ and
$\omega$ are chosen to be special values. Some applications of our results in
random matrix theory are also discussed.

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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
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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: quant-ph
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The categories of this paper are: cond-mat