Numerical Approach to Painlevé Transcendents on Unbounded Domains

A multidomain spectral approach for Painlevé transcendents on unbounded domains is presented. This method is designed to study solutions determined uniquely by a possibly divergent asymptotic series valid near infinity in a sector and approximates the solution on straight lines lying entirely within...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2018
Main Authors: Klein, C., Stoilov, N.
Format: Article
Language:English
Published: Інститут математики НАН України 2018
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/209782
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Numerical Approach to Painlevé Transcendents on Unbounded Domains / C. Klein, N. Stoilov // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 31 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-209782
record_format dspace
spelling Klein, C.
Stoilov, N.
2025-11-26T12:19:57Z
2018
Numerical Approach to Painlevé Transcendents on Unbounded Domains / C. Klein, N. Stoilov // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 31 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 34M55; 65L10
arXiv: 1807.04442
https://nasplib.isofts.kiev.ua/handle/123456789/209782
https://doi.org/10.3842/SIGMA.2018.068
A multidomain spectral approach for Painlevé transcendents on unbounded domains is presented. This method is designed to study solutions determined uniquely by a possibly divergent asymptotic series valid near infinity in a sector and approximates the solution on straight lines lying entirely within said sector without the need to evaluate truncations of the series at any finite point. The accuracy of the method is illustrated for the example of the tritronquée solution to the Painlevé I equation.
This work was partially supported by the PARI and FEDER programs in 2016 and 2017, by the ANR-FWF project ANuI, and by the Marie-Curie RISE network IPaDEGAN. We thank M. Fasondini for helpful remarks. We are grateful to the anonymous referee for his constructive refereeing and many useful suggestions.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Numerical Approach to Painlevé Transcendents on Unbounded Domains
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Numerical Approach to Painlevé Transcendents on Unbounded Domains
spellingShingle Numerical Approach to Painlevé Transcendents on Unbounded Domains
Klein, C.
Stoilov, N.
title_short Numerical Approach to Painlevé Transcendents on Unbounded Domains
title_full Numerical Approach to Painlevé Transcendents on Unbounded Domains
title_fullStr Numerical Approach to Painlevé Transcendents on Unbounded Domains
title_full_unstemmed Numerical Approach to Painlevé Transcendents on Unbounded Domains
title_sort numerical approach to painlevé transcendents on unbounded domains
author Klein, C.
Stoilov, N.
author_facet Klein, C.
Stoilov, N.
publishDate 2018
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description A multidomain spectral approach for Painlevé transcendents on unbounded domains is presented. This method is designed to study solutions determined uniquely by a possibly divergent asymptotic series valid near infinity in a sector and approximates the solution on straight lines lying entirely within said sector without the need to evaluate truncations of the series at any finite point. The accuracy of the method is illustrated for the example of the tritronquée solution to the Painlevé I equation.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/209782
citation_txt Numerical Approach to Painlevé Transcendents on Unbounded Domains / C. Klein, N. Stoilov // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 31 назв. — англ.
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first_indexed 2025-12-07T18:02:08Z
last_indexed 2025-12-07T18:02:08Z
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