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.

引用

页码：504 / 547

页数：44

共 50 条

[1] Connection formulas for the Ablowitz-Segur solutions of the inhomogeneous Painleve II equation
Dai, Dan
Hu, Weiying
NONLINEARITY, 2017, 30 (07) : 2982 - 3009
[2] On the location of poles for the Ablowitz-Segur family of solutions to the second Painleve equation
Bertola, M.
NONLINEARITY, 2012, 25 (04)
[3] The τ-function of the Ablowitz-Segur family of solutions to Painleve II as a Widom constant
Desiraju, Harini
JOURNAL OF MATHEMATICAL PHYSICS, 2019, 60 (11)
[4] On the quasi-Ablowitz-Segur and quasi-Hastings-McLeod solutions of the inhomogeneous Painleve II equation
Dai, Dan
Hu, Weiying
RANDOM MATRICES-THEORY AND APPLICATIONS, 2018, 7 (04)
[5] On an exact WKB approach to Ablowitz-Segur's connection problem for the second Painleve equation
Takei, Y
ANZIAM JOURNAL, 2002, 44 : 111 - 119
[6] Total integrals of global solutions to Painleve II
Baik, Jinho
Buckingham, Robert
DiFranco, Jeffery
Its, Alexander
NONLINEARITY, 2009, 22 (05) : 1021 - 1061
[7] Solitary wave solutions along with Painleve analysis for the Ablowitz-Kaup-Newell-Segur water waves equation
Rizvi, Syed T. R.
Seadawy, Aly R.
Akram, U.
Younis, M.
Althobaiti, Ali
MODERN PHYSICS LETTERS B, 2022, 36 (02):
[8] Singular asymptotics for solutions of the inhomogeneous Painleve II equation
Hu, Weiying
NONLINEARITY, 2019, 32 (10) : 3843 - 3872
[9] On integrals of the tronquee solutions and the associated Hamiltonians for the Painleve II equation
Dai, Dan
Xu, Shuai-Xia
Zhang, Lun
JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 269 (03) : 2430 - 2476
[10] Jacobian elliptic wave solutions for the Wadati-Segur-Ablowitz equation
Teh, CGR
Koo, WK
Lee, BS
INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 1997, 11 (23): : 2849 - 2854

← 1 2 3 4 5 →