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• W2966734350 abstract "We consider a family of tronqu'{e}e solutions of the Painelv'{e} II equation begin{equation*} q''(s)=2q(s)^3+sq(s)-(2alpha+frac12), qquad alpha > -frac12, end{equation*} which is characterized by the Stokes multipliers $$s_1=-e^{-2alpha pi i },quad s_2=omega, quad s_3=-e^{2 alpha pi i} $$ 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." @default.
• W2966734350 created "2019-08-13" @default.
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• W2966734350 date "2019-08-05" @default.
• W2966734350 modified "2023-09-26" @default.
• W2966734350 title "On integrals of the tronqu'{e}e solutions and the associated Hamiltonians for the Painlev'{e} II equation" @default.
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• W2966734350 doi "https://doi.org/10.48550/arxiv.1908.01532" @default.
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