Boutroux Ansatz for the Degenerate Third Painleve Transcendents

被引：0

作者：

Shimomura, Shun ^{[1
]}

机构：

[1] Keio Univ, Dept Math, 3-14-1 Hiyoshi,Kohoku Ku, Yokohama 2238522, Japan

来源：

PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES | 2024年 / 60卷 / 04期

关键词：

degenerate third Painleve equation; Boutroux ansatz; Boutroux equations; isomonodromy deformation; WKB analysis; pe-function; theta-function; CONNECTION PROBLEM; ASYMPTOTICS; EQUATIONS; FORMULAS;

D O I：

10.4171/PRIMS/60-4-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a general solution of the degenerate third Painleve<acute accent> equation we show the Boutroux ansatz near the point at infinity. It admits an asymptotic representation in terms of the Weierstrass pe-function in cheese-like strips along generic directions. The expression is obtained by using isomonodromy deformation of a linear system governed by the degenerate third Painleve equation.

引用

页码：651 / 698

页数：48

共 50 条

[1] THE BOUTROUX ANSATZ FOR THE 2ND PAINLEVE EQUATION IN THE COMPLEX-DOMAIN
NOVOKSHENOV, VY
MATHEMATICS OF THE USSR-IZVESTIYA, 1990, 54 (06): : 587 - 609
[2] On WKB Theoretic Transformations for Painleve Transcendents on Degenerate Stokes Segments
Iwaki, Kohei
PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 2015, 51 (01) : 1 - 57
[3] Growth of modified Painleve transcendents of the fifth and the third kind
Shimomura, S
FORUM MATHEMATICUM, 2004, 16 (02) : 231 - 247
[4] Value distribution of the third Painleve transcendents in sectorial domains
Sasaki, Yoshikatsu
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 2007, 83 (06) : 79 - 82
[5] FREQUENCY OF a-POINTS FOR THE FIFTH AND THE THIRD PAINLEVE TRANSCENDENTS IN A SECTOR
Shimomura, Shun
TOHOKU MATHEMATICAL JOURNAL, 2013, 65 (04) : 591 - 605
[6] ASYMPTOTIC BEHAVIOUR OF THE THIRD PAINLEVE TRANSCENDENTS IN THE SPACE OF INITIAL VALUES
Joshi, Nalini
Radnovic, Milena
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2019, 372 (09) : 6507 - 6546
[7] EQUI-DISTRIBUTION OF VALUES FOR THE THIRD AND THE FIFTH PAINLEVE TRANSCENDENTS
Shimomura, Shun
NAGOYA MATHEMATICAL JOURNAL, 2008, 192 : 89 - 109
[8] Hankel determinants for a singular complex weight and the first and third Painleve transcendents
Xu, Shuai-Xia
Dai, Dan
Zhao, Yu-Qiu
JOURNAL OF APPROXIMATION THEORY, 2016, 205 : 64 - 92
[9] Tabulation of Painleve 6 transcendents
Guzzetti, Davide
NONLINEARITY, 2012, 25 (12) : 3235 - 3276
[10] A UNIFIED APPROACH TO THE PAINLEVE TRANSCENDENTS
Steinmetz, Norbert
ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 2017, 42 (01) : 17 - 49

← 1 2 3 4 5 →