On Some Hamiltonian Properties of the Isomonodromic Tau Functions

DOI10.1142/S0129055X18400081zbMath1408.30036arXiv1803.04212OpenAlexW4246324783MaRDI QIDQ4611502

Alexander R. Its, Andrei Prokhorov

Publication date: 18 January 2019

Published in: Reviews in Mathematical Physics, Ludwig Faddeev Memorial Volume (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.04212

zbMATH Keywords

differential equationsrational matrix functionsJimbo-Miwa-Ueno tau function

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Meromorphic functions of one complex variable (general theory) (30D30) Linear ordinary differential equations and systems in the complex domain (34M03)

Related Items (12)

Painlevé/CFT correspondence on a torus ⋮ Relations between different Hamiltonian forms of the third Painlevé equation ⋮ On integrals of the tronquée solutions and the associated Hamiltonians for the Painlevé II equation ⋮ Isomonodromic deformations: confluence, reduction and quantisation ⋮ Monodromy dependence and symplectic geometry of isomonodromic tau functions on the torus ⋮ Hamiltonian structure of rational isomonodromic deformation systems ⋮ Short distance asymptotics for a generalized two-point scaling function in the two-dimensional Ising model ⋮ Isomonodromic deformations of a rational differential system and reconstruction with the topological recursion: The sl2 case ⋮ Tau-functions and monodromy symplectomorphisms ⋮ Irregular conformal blocks and connection formulae for Painlevé V functions ⋮ From Heun class equations to Painlevé equations ⋮ Gaussian unitary ensemble with jump discontinuities and the coupled Painlevé II and IV systems

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