The Painlevé I hierarchy: Correspondence between the isomonodromic approach and the minimal models of the KP hierarchy
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918130533531648 |
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| author | Alameddine, Mohamad Hayford, Nathan Marchal, Olivier |
| author_facet | Alameddine, Mohamad Hayford, Nathan Marchal, Olivier |
| contents | Two approaches to the Painlevé I hierarchy are discussed: the isomonodromic construction based on meromorphic connections, and the minimal models construction based on a reduction of the KP hierarchy. An explicit correspondence between both formalisms is built which gives the identification of these setups. In particular, this provides new expressions for the Lax matrices and Hamiltonians. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_18433 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Painlevé I hierarchy: Correspondence between the isomonodromic approach and the minimal models of the KP hierarchy Alameddine, Mohamad Hayford, Nathan Marchal, Olivier Mathematical Physics Symplectic Geometry Exactly Solvable and Integrable Systems Two approaches to the Painlevé I hierarchy are discussed: the isomonodromic construction based on meromorphic connections, and the minimal models construction based on a reduction of the KP hierarchy. An explicit correspondence between both formalisms is built which gives the identification of these setups. In particular, this provides new expressions for the Lax matrices and Hamiltonians. |
| title | The Painlevé I hierarchy: Correspondence between the isomonodromic approach and the minimal models of the KP hierarchy |
| topic | Mathematical Physics Symplectic Geometry Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2508.18433 |