A family of solutions of a higher order PVI equation near a regular singularity

Shun Shimomura

doi:10.1088/0305-4470/39/39/S09

A family of solutions of a higher order PVI equation near a regular singularity

Shun Shimomura

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Restriction of the N-dimensional Garnier system to a complex line yields a system of second-order nonlinear differential equations, which may be regarded as a higher order version of the sixth Painlevé equation. Near a regular singularity of the system, we present a 2N-parameter family of solutions expanded into convergent series. These solutions are constructed by iteration, and their convergence is proved by using a kind of majorant series. For simplicity, we describe the proof in the case N ≤ 2.

Original language	English
Article number	S09
Pages (from-to)	12153-12165
Number of pages	13
Journal	Journal of Physics A: Mathematical and General
Volume	39
Issue number	39
DOIs	https://doi.org/10.1088/0305-4470/39/39/S09
Publication status	Published - 2006 Sept 29

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy(all)

Access to Document

10.1088/0305-4470/39/39/S09

Cite this

@article{8227d325e0d944438e23cffd2b4da67f,

title = "A family of solutions of a higher order PVI equation near a regular singularity",

abstract = "Restriction of the N-dimensional Garnier system to a complex line yields a system of second-order nonlinear differential equations, which may be regarded as a higher order version of the sixth Painlev{\'e} equation. Near a regular singularity of the system, we present a 2N-parameter family of solutions expanded into convergent series. These solutions are constructed by iteration, and their convergence is proved by using a kind of majorant series. For simplicity, we describe the proof in the case N ≤ 2.",

author = "Shun Shimomura",

year = "2006",

month = sep,

day = "29",

doi = "10.1088/0305-4470/39/39/S09",

language = "English",

volume = "39",

pages = "12153--12165",

journal = "Journal of Physics A: Mathematical and Theoretical",

issn = "1751-8113",

publisher = "IOP Publishing Ltd.",

number = "39",

}

TY - JOUR

T1 - A family of solutions of a higher order PVI equation near a regular singularity

AU - Shimomura, Shun

PY - 2006/9/29

Y1 - 2006/9/29

N2 - Restriction of the N-dimensional Garnier system to a complex line yields a system of second-order nonlinear differential equations, which may be regarded as a higher order version of the sixth Painlevé equation. Near a regular singularity of the system, we present a 2N-parameter family of solutions expanded into convergent series. These solutions are constructed by iteration, and their convergence is proved by using a kind of majorant series. For simplicity, we describe the proof in the case N ≤ 2.

AB - Restriction of the N-dimensional Garnier system to a complex line yields a system of second-order nonlinear differential equations, which may be regarded as a higher order version of the sixth Painlevé equation. Near a regular singularity of the system, we present a 2N-parameter family of solutions expanded into convergent series. These solutions are constructed by iteration, and their convergence is proved by using a kind of majorant series. For simplicity, we describe the proof in the case N ≤ 2.

UR - http://www.scopus.com/inward/record.url?scp=33748773348&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33748773348&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/39/39/S09

DO - 10.1088/0305-4470/39/39/S09

M3 - Article

AN - SCOPUS:33748773348

SN - 1751-8113

VL - 39

SP - 12153

EP - 12165

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 39

M1 - S09

ER -

A family of solutions of a higher order PVI equation near a regular singularity

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this