Elliptic asymptotics for the complete third Painlevé transcendents
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912232362737664 |
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| author | Shimomura, Shun |
| author_facet | Shimomura, Shun |
| contents | For a general solution of the third Painlevé equation of complete type we show the Boutroux ansatz near the point at infinity. It admits an asymptotic representation in terms of the Jacobi sn-function in cheese-like strips along generic directions. The expression is derived by using isomonodromy deformation of a linear system governed by the third Painlevé equation of this type. In our calculation of the WKB analysis, the treated Stokes curve ranges on both upper and lower sheets of the two sheeted Riemann surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_00886 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Elliptic asymptotics for the complete third Painlevé transcendents Shimomura, Shun Classical Analysis and ODEs 34M55, 34M56, 34M40, 34M60 For a general solution of the third Painlevé equation of complete type we show the Boutroux ansatz near the point at infinity. It admits an asymptotic representation in terms of the Jacobi sn-function in cheese-like strips along generic directions. The expression is derived by using isomonodromy deformation of a linear system governed by the third Painlevé equation of this type. In our calculation of the WKB analysis, the treated Stokes curve ranges on both upper and lower sheets of the two sheeted Riemann surface. |
| title | Elliptic asymptotics for the complete third Painlevé transcendents |
| topic | Classical Analysis and ODEs 34M55, 34M56, 34M40, 34M60 |
| url | https://arxiv.org/abs/2211.00886 |