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

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Abstract

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)
Volume13
DOIs
Publication statusPublished - 2017 Apr 15

Keywords

  • Lax equations
  • Multi-Poisson structure
  • Painlevé equations

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Geometry and Topology

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