Browsing by Subject "Riemann-Hilbert correspondence"

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    Connection Problem for Painlevé Tau Functions
    (2019-08) Prokhorov, Andrei; Its, Alexander; Bleher, Pavel; Eremenko, Alexandre; Tarasov, Vitaly
    We derive the differential identities for isomonodromic tau functions, describing their monodromy dependence. For Painlev´e equations we obtain them from the relation of tau function to classical action which is a consequence of quasihomogeneity of corresponding Hamiltonians. We use these identities to solve the connection problem for generic solution of Painlev´e-III(D8) equation, and homogeneous Painlev´e-II equation. We formulate conjectures on Hamiltonian and symplectic structure of general isomonodromic deformations we obtained during our studies and check them for Painlev´e equations.