Connection Problem for Painlevé tau Functions
thesisposted on 16.10.2019, 16:19 by Andrei ProkhorovAndrei Prokhorov
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 iso\-mo\-no\-dro\-mic deformations we obtained during our studies and check them for Painlev\'e equations.
Development of methods of spectral analysis, scattering theory and integrable systems in modern problems of mathematical physics.
Russian Science FoundationFind out more...
Degree TypeDoctor of Philosophy
Advisor/Supervisor/Committee ChairAlexander Its
Additional Committee Member 2Pavel Bleher
Additional Committee Member 3Alexandre Eremenko
Additional Committee Member 4Vitaly Tarasov
Painlev\'e equationsisomonodromic tau functionconnection problemHamiltonian systemsclassical actionquasihomogeneous functionRiemann-Hilbert correspondenceisomonodromic deformationsMathematical Physics not elsewhere classifiedIntegrable Systems (Classical and Quantum)Ordinary Differential Equations, Difference Equations and Dynamical Systems