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

被引：4
|
作者：
Kokocki, Piotr [1 ]
机构：
[1] Nicolaus Copernicus Univ, Fac Math & Comp Sci, Chopina 12-18, PL-87100 Torun, Poland
来源：
STUDIES IN APPLIED MATHEMATICS | 2020年 / 144卷 / 04期
关键词：
asymptotic expansion; geometric flow; Painleve II equation; Riemann-Hilbert-problem; ASYMPTOTICS;
D O I：
10.1111/sapm.12307
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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.
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页码：504 / 547
页数：44
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