Elliptic asymptotic representation of the fifth Painlevé transcendents
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866915868584181760 |
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| author | Shimomura, Shun |
| author_facet | Shimomura, Shun |
| contents | For the fifth Painlevé transcendents an asymptotic representation by the Jacobi $\mathrm{sn}$-function is presented in cheese-like strips along generic directions near the point at infinity. Its elliptic main part may be understood to depend on the phase shift as a single integration constant, which is parametrised by monodromy data for the associated isomonodromy deformation. The other integration constant is contained in the error term or in a correction function. This paper contains corrections of the Stokes graph and of the related results in the early version. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2012_07321 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Elliptic asymptotic representation of the fifth Painlevé transcendents Shimomura, Shun Classical Analysis and ODEs Mathematical Physics 34M55, 34M56, 34M40, 34M60, 33E05 For the fifth Painlevé transcendents an asymptotic representation by the Jacobi $\mathrm{sn}$-function is presented in cheese-like strips along generic directions near the point at infinity. Its elliptic main part may be understood to depend on the phase shift as a single integration constant, which is parametrised by monodromy data for the associated isomonodromy deformation. The other integration constant is contained in the error term or in a correction function. This paper contains corrections of the Stokes graph and of the related results in the early version. |
| title | Elliptic asymptotic representation of the fifth Painlevé transcendents |
| topic | Classical Analysis and ODEs Mathematical Physics 34M55, 34M56, 34M40, 34M60, 33E05 |
| url | https://arxiv.org/abs/2012.07321 |