Logarithmic solutions of the fifth painlevé equation near the origin

Shun Shimomura

研究成果: Article

1 引用 (Scopus)

抄録

For the fifth Painlevé equation near the origin we present two kinds of logarithmic solutions, which are represented, respectively, by convergent series with multipliers admitting asymptotic expansions in descending logarithmic powers and by those with multipliers polynomial in logarithmic powers. It is conjectured that the asymptotic multipliers are also polynomials in logarithmic powers. These solutions are constructed by iteration on certain rings of exponential type series.

元の言語English
ページ(範囲)797-825
ページ数29
ジャーナルTokyo Journal of Mathematics
39
発行部数3
出版物ステータスPublished - 2017 3 1

Fingerprint

Logarithmic
Multiplier
Polynomial
Exponential Type
Series
Asymptotic Expansion
Iteration
Ring

ASJC Scopus subject areas

  • Mathematics(all)

これを引用

Logarithmic solutions of the fifth painlevé equation near the origin. / Shimomura, Shun.

:: Tokyo Journal of Mathematics, 巻 39, 番号 3, 01.03.2017, p. 797-825.

研究成果: Article

Shimomura, Shun. / Logarithmic solutions of the fifth painlevé equation near the origin. :: Tokyo Journal of Mathematics. 2017 ; 巻 39, 番号 3. pp. 797-825.
@article{1f1aefe7662e4a318b943d8bf5de5d17,
title = "Logarithmic solutions of the fifth painlev{\'e} equation near the origin",
abstract = "For the fifth Painlev{\'e} equation near the origin we present two kinds of logarithmic solutions, which are represented, respectively, by convergent series with multipliers admitting asymptotic expansions in descending logarithmic powers and by those with multipliers polynomial in logarithmic powers. It is conjectured that the asymptotic multipliers are also polynomials in logarithmic powers. These solutions are constructed by iteration on certain rings of exponential type series.",
keywords = "Logarithmic solutions, Painlev{\'e} equation",
author = "Shun Shimomura",
year = "2017",
month = "3",
day = "1",
language = "English",
volume = "39",
pages = "797--825",
journal = "Tokyo Journal of Mathematics",
issn = "0387-3870",
publisher = "Publication Committee for the Tokyo Journal of Mathematics",
number = "3",

}

TY - JOUR

T1 - Logarithmic solutions of the fifth painlevé equation near the origin

AU - Shimomura, Shun

PY - 2017/3/1

Y1 - 2017/3/1

N2 - For the fifth Painlevé equation near the origin we present two kinds of logarithmic solutions, which are represented, respectively, by convergent series with multipliers admitting asymptotic expansions in descending logarithmic powers and by those with multipliers polynomial in logarithmic powers. It is conjectured that the asymptotic multipliers are also polynomials in logarithmic powers. These solutions are constructed by iteration on certain rings of exponential type series.

AB - For the fifth Painlevé equation near the origin we present two kinds of logarithmic solutions, which are represented, respectively, by convergent series with multipliers admitting asymptotic expansions in descending logarithmic powers and by those with multipliers polynomial in logarithmic powers. It is conjectured that the asymptotic multipliers are also polynomials in logarithmic powers. These solutions are constructed by iteration on certain rings of exponential type series.

KW - Logarithmic solutions

KW - Painlevé equation

UR - http://www.scopus.com/inward/record.url?scp=85017358511&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85017358511&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85017358511

VL - 39

SP - 797

EP - 825

JO - Tokyo Journal of Mathematics

JF - Tokyo Journal of Mathematics

SN - 0387-3870

IS - 3

ER -