Truncated Solutions of Painlevé Equation Pv
We obtain convergent representations (as Borel summed transseries) for the five one-parameter families of truncated solutions of the fifth Painlevé equation with nonzero parameters, valid in half planes, for large independent variable. We also find the position of the first array of poles, bordering...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2018 |
| ISSN: | 1815-0659 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209840 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Truncated Solutions of Painlevé Equation Pv / R.D. Costin // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 38 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862609162795483136 |
|---|---|
| author | Costin, R.D. |
| author_facet | Costin, R.D. |
| citation_txt | Truncated Solutions of Painlevé Equation Pv / R.D. Costin // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 38 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We obtain convergent representations (as Borel summed transseries) for the five one-parameter families of truncated solutions of the fifth Painlevé equation with nonzero parameters, valid in half planes, for large independent variable. We also find the position of the first array of poles, bordering the region of analyticity. For a special value of this parameter, they represent tri-truncated solutions, analytic in almost the full complex plane, for a large independent variable. A brief historical note and references on truncated solutions of the other Painlevé equations are also included.
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| first_indexed | 2025-12-07T12:54:10Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209840 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T12:54:10Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Costin, R.D. 2025-11-27T14:47:47Z 2018 Truncated Solutions of Painlevé Equation Pv / R.D. Costin // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 38 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33E17; 34M30; 34M25 arXiv: 1804.11273 https://nasplib.isofts.kiev.ua/handle/123456789/209840 https://doi.org/10.3842/SIGMA.2018.117 We obtain convergent representations (as Borel summed transseries) for the five one-parameter families of truncated solutions of the fifth Painlevé equation with nonzero parameters, valid in half planes, for large independent variable. We also find the position of the first array of poles, bordering the region of analyticity. For a special value of this parameter, they represent tri-truncated solutions, analytic in almost the full complex plane, for a large independent variable. A brief historical note and references on truncated solutions of the other Painlevé equations are also included. The author is grateful to the editors for valuable references and information, and to the referees careful reading of the manuscript and for their helpful comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Truncated Solutions of Painlevé Equation Pv Article published earlier |
| spellingShingle | Truncated Solutions of Painlevé Equation Pv Costin, R.D. |
| title | Truncated Solutions of Painlevé Equation Pv |
| title_full | Truncated Solutions of Painlevé Equation Pv |
| title_fullStr | Truncated Solutions of Painlevé Equation Pv |
| title_full_unstemmed | Truncated Solutions of Painlevé Equation Pv |
| title_short | Truncated Solutions of Painlevé Equation Pv |
| title_sort | truncated solutions of painlevé equation pv |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209840 |
| work_keys_str_mv | AT costinrd truncatedsolutionsofpainleveequationpv |