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arXiv · 1808.09039

Total integrals of Ablowitz-Segur solutions for the inhomogeneous Painlev\'e II equation

Piotr Kokocki
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Abstract

In this paper, we establish a formula determining the value of the Cauchy integrals of the real and purely imaginary Ablowitz-Segur solutions for the inhomogeneous second Painlev\'e equation. Our approach relies on the analysis of the corresponding Riemann-Hilbert problem and the construction of an appropriate parametrix in a neighborhood of the origin. Obtained integral formulas are consistent with already known analogous results for Ablowitz-Segur solutions of homogeneous Painlev\'e II equation.

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Piotr Kokocki. 2018-08-27. Total integrals of Ablowitz-Segur solutions for the inhomogeneous Painlev\'e II equation. https://arxiv.org/abs/1808.09039

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