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arXiv · 2508.18433

The Painlev\'{e} I hierarchy: Correspondence between the isomonodromic approach and the minimal models of the KP hierarchy

Mohamad Alameddine·Nathan Hayford·Olivier Marchal
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Abstract

Two approaches to the Painlev\'{e} 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.

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Mohamad Alameddine, Nathan Hayford, Olivier Marchal. 2025-08-25. The Painlev\'{e} I hierarchy: Correspondence between the isomonodromic approach and the minimal models of the KP hierarchy. https://arxiv.org/abs/2508.18433

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