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