On the asymptotics of real solutions for the Painlevé I equation
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909306122665984 |
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| author | Long, Wen-Gao Xia, Jun |
| author_facet | Long, Wen-Gao Xia, Jun |
| contents | In this paper, we revisit the asymptotic formulas of real Painlevé I transcendents as the independent variable tends to negative infinity, which were initially derived by Kapaev with the complex WKB method. Using the Riemann-Hilbert method, we improve the error estimates of the oscillatory type asymptotics and provide precise error estimates of the singular type asymptotics. We also establish the corresponding asymptotics for the associated Hamiltonians of real Painlevé I transcendents. In addition, two typos in the mentioned asymptotic behaviors in literature are corrected. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03313 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the asymptotics of real solutions for the Painlevé I equation Long, Wen-Gao Xia, Jun Classical Analysis and ODEs In this paper, we revisit the asymptotic formulas of real Painlevé I transcendents as the independent variable tends to negative infinity, which were initially derived by Kapaev with the complex WKB method. Using the Riemann-Hilbert method, we improve the error estimates of the oscillatory type asymptotics and provide precise error estimates of the singular type asymptotics. We also establish the corresponding asymptotics for the associated Hamiltonians of real Painlevé I transcendents. In addition, two typos in the mentioned asymptotic behaviors in literature are corrected. |
| title | On the asymptotics of real solutions for the Painlevé I equation |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2409.03313 |