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<p>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 established, identifying these setups explicitly. In particular, this yields new expressions for the Lax matrices and Hamiltonians.</p>

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The Painlevé I Hierarchy: Correspondence Between the Isomonodromic Approach and the Minimal Models of the KP Hierarchy

  • 期刊论文

  • 发表日期：

    2026年2月6日

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  • Mohamad Alameddine,
  • Nathan Hayford,
  • Olivier Marchal

摘要

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 established, identifying these setups explicitly. In particular, this yields new expressions for the Lax matrices and Hamiltonians.