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 |
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| Date: | 2018 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| 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| _version_ | 1862716022428008448 |
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| author | Klein, C. Stoilov, N. |
| author_facet | Klein, C. Stoilov, N. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T18:02:08Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-209782 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:02:08Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| 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 |
| spellingShingle | Numerical Approach to Painlevé Transcendents on Unbounded Domains Klein, C. Stoilov, N. |
| title | 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_short | Numerical Approach to Painlevé Transcendents on Unbounded Domains |
| title_sort | numerical approach to painlevé transcendents on unbounded domains |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209782 |
| work_keys_str_mv | AT kleinc numericalapproachtopainlevetranscendentsonunboundeddomains AT stoilovn numericalapproachtopainlevetranscendentsonunboundeddomains |