TY - JOUR

T1 - Multi-poisson approach to the Painlevé equations

T2 - From the isospectral deformation to the isomonodromic deformation

AU - Chiba, Hayato

N1 - Publisher Copyright:
© 2017, Institute of Mathematics. All rights reserved.

PY - 2017/4/15

Y1 - 2017/4/15

N2 - 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.

AB - 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.

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U2 - 10.3842/SIGMA.2017.025

DO - 10.3842/SIGMA.2017.025

M3 - Article

AN - SCOPUS:85019608552

SN - 1815-0659

VL - 13

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

M1 - 025

ER -