Total integrals of Ablowitz-Segur solutions for the inhomogeneous Painleve II equation

摘要

In this paper, we establish a formula determining the value of the Cauchy principal value integrals of the real and purely imaginary Ablowitz-Segur solutions for the inhomogeneous second Painleve 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 the Ablowitz-Segur solutions of the homogeneous Painleve II equation.