Riemann-Hilbert characterisation of Painlevé 5 asymptotics and nonlinear monodromy-Stokes structure
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915943987281920 |
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| author | Shimomura, Shun |
| author_facet | Shimomura, Shun |
| contents | For a generic Painlevé 5 equation we characterise all the asymptotics in a right half plane near the point at infinity, that is, we find classified explicit solutions that are, by the Riemann-Hilbert correspondence, labelled with monodromy data filling up the whole monodromy manifold. To do so, in addition to the asymptotics by Andreev and Kitaev along the positive real axis, we require elliptic asymptotics along generic directions and newly provided truncated solutions arising from a general solution along the imaginary axes. To know analytic continuations outside this region we formulate a nonlinear monodromy-Stokes structure, which is observed as changes of monodromy data contained in the explicit expressions of solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01385 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Riemann-Hilbert characterisation of Painlevé 5 asymptotics and nonlinear monodromy-Stokes structure Shimomura, Shun Classical Analysis and ODEs 34M55, 34M56, 34M40 For a generic Painlevé 5 equation we characterise all the asymptotics in a right half plane near the point at infinity, that is, we find classified explicit solutions that are, by the Riemann-Hilbert correspondence, labelled with monodromy data filling up the whole monodromy manifold. To do so, in addition to the asymptotics by Andreev and Kitaev along the positive real axis, we require elliptic asymptotics along generic directions and newly provided truncated solutions arising from a general solution along the imaginary axes. To know analytic continuations outside this region we formulate a nonlinear monodromy-Stokes structure, which is observed as changes of monodromy data contained in the explicit expressions of solutions. |
| title | Riemann-Hilbert characterisation of Painlevé 5 asymptotics and nonlinear monodromy-Stokes structure |
| topic | Classical Analysis and ODEs 34M55, 34M56, 34M40 |
| url | https://arxiv.org/abs/2509.01385 |