Multi-poisson approach to the Painlevé equations: From the isospectral deformation to the isomonodromic deformation

Hayato Chiba

Research output: Contribution to journalArticle


A multi-Poisson structure on a Lie algebra g provides a systematic way to construct completely integrable Hamiltonian systems on g expressed in Lax form ∂Xλ/∂t = [Xλ, Aλ] in the sense of the isospectral deformation, where Xλ, Aλ ∈ g depend rationally on the indeterminate λ called the spectral parameter. In this paper, a method for modifying the isospectral deformation equation to the Lax equation ∂Xλ/∂t = [Xλ, Aλ] + ∂Aλ/∂λ in the sense of the isomonodromic deformation, which exhibits the Painlevé property, is proposed. This method gives a few new Painlevé systems of dimension four.

Original languageEnglish
Article number025
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Publication statusPublished - Apr 15 2017


All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematical Physics
  • Geometry and Topology

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