Total integrals of Ablowitz-Segur solutions for the inhomogeneous Painlev\'e II equation
Classical Analysis and ODEs
2019-09-02 v6
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.
Keywords
Cite
@article{arxiv.1808.09039,
title = {Total integrals of Ablowitz-Segur solutions for the inhomogeneous Painlev\'e II equation},
author = {Piotr Kokocki},
journal= {arXiv preprint arXiv:1808.09039},
year = {2019}
}
Comments
The results concerning applications to fluid dynamics are moved to forthcoming publication