Trans-Series Asymptotics of Solutions to the Degenerate Painlevé III Equation: A Case Study
A one-parameter family of trans-series asymptotics as τ → ±∞ and τ → ±i∞ for solutions of the degenerate Painlevé III equation (DP3E), ′′(τ) = (′(τ))²/(τ) − ′(τ)/τ + 1/τ(−8ε(u(τ))² + 2) + ²/(τ), where ε ∈ {±1}, ∈ ℂ, and ∈ ℝ∖{0}, are parametrised in terms of the monodromy data of an associated firs...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2025 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2025
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/214097 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Trans-Series Asymptotics of Solutions to the Degenerate Painlevé III Equation: A Case Study. Arthur Vartanian. SIGMA 21 (2025), 067, 135 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862661681685987328 |
|---|---|
| author | Vartanian, Arthur |
| author_facet | Vartanian, Arthur |
| citation_txt | Trans-Series Asymptotics of Solutions to the Degenerate Painlevé III Equation: A Case Study. Arthur Vartanian. SIGMA 21 (2025), 067, 135 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | A one-parameter family of trans-series asymptotics as τ → ±∞ and τ → ±i∞ for solutions of the degenerate Painlevé III equation (DP3E), ′′(τ) = (′(τ))²/(τ) − ′(τ)/τ + 1/τ(−8ε(u(τ))² + 2) + ²/(τ), where ε ∈ {±1}, ∈ ℂ, and ∈ ℝ∖{0}, are parametrised in terms of the monodromy data of an associated first-order 2 × 2 matrix linear ODE via the isomonodromy deformation approach: trans-series asymptotics for the associated Hamiltonian and principal auxiliary functions and the solution of one of the σ-forms of the DP3E are also obtained. The actions of various Lie-point symmetries for the DP3E are derived.
|
| first_indexed | 2026-03-16T05:00:15Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-214097 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-16T05:00:15Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Vartanian, Arthur 2026-02-19T11:14:35Z 2025 Trans-Series Asymptotics of Solutions to the Degenerate Painlevé III Equation: A Case Study. Arthur Vartanian. SIGMA 21 (2025), 067, 135 pages 1815-0659 2020 Mathematics Subject Classification: 33E17; 34M35; 34M40; 34M50; 34M55; 34M56; 34M60 arXiv:2010.11235 https://nasplib.isofts.kiev.ua/handle/123456789/214097 https://doi.org/10.3842/SIGMA.2025.067 A one-parameter family of trans-series asymptotics as τ → ±∞ and τ → ±i∞ for solutions of the degenerate Painlevé III equation (DP3E), ′′(τ) = (′(τ))²/(τ) − ′(τ)/τ + 1/τ(−8ε(u(τ))² + 2) + ²/(τ), where ε ∈ {±1}, ∈ ℂ, and ∈ ℝ∖{0}, are parametrised in terms of the monodromy data of an associated first-order 2 × 2 matrix linear ODE via the isomonodromy deformation approach: trans-series asymptotics for the associated Hamiltonian and principal auxiliary functions and the solution of one of the σ-forms of the DP3E are also obtained. The actions of various Lie-point symmetries for the DP3E are derived. The author is grateful to A.V. Kitaev for perspicacious comments and criticisms related to preliminary results of this work, and to the St. Petersburg Branch of the Steklov Mathematical Institute (POMI) for hospitality. The author is grateful to the referees for a cornucopia of constructive recommendations, which were instrumental in improving the content of the paper. The author also wishes to honour the memories of L.D. Faddeev and P.P. Kulish. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Trans-Series Asymptotics of Solutions to the Degenerate Painlevé III Equation: A Case Study Article published earlier |
| spellingShingle | Trans-Series Asymptotics of Solutions to the Degenerate Painlevé III Equation: A Case Study Vartanian, Arthur |
| title | Trans-Series Asymptotics of Solutions to the Degenerate Painlevé III Equation: A Case Study |
| title_full | Trans-Series Asymptotics of Solutions to the Degenerate Painlevé III Equation: A Case Study |
| title_fullStr | Trans-Series Asymptotics of Solutions to the Degenerate Painlevé III Equation: A Case Study |
| title_full_unstemmed | Trans-Series Asymptotics of Solutions to the Degenerate Painlevé III Equation: A Case Study |
| title_short | Trans-Series Asymptotics of Solutions to the Degenerate Painlevé III Equation: A Case Study |
| title_sort | trans-series asymptotics of solutions to the degenerate painlevé iii equation: a case study |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214097 |
| work_keys_str_mv | AT vartanianarthur transseriesasymptoticsofsolutionstothedegeneratepainleveiiiequationacasestudy |