Multi-Poisson Approach to the Painlevé Equations: from the Isospectral Deformation to the Isomonodromic Deformation

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2017
• Main Author: Chiba, H.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2017
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/148562
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Multi-Poisson Approach to the Painlevé Equations: from the Isospectral Deformation to the Isomonodromic Deformation / H. Chiba // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 18 назв. — англ.

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. I...