Prokhorov_dissertation.pdf (759.38 kB)
Connection Problem for Painlevé tau Functions
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.
Funding
Development of methods of spectral analysis, scattering theory and integrable systems in modern problems of mathematical physics.
Russian Science Foundation
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Degree Type
- Doctor of Philosophy
Department
- Mathematics
Campus location
- Indianapolis
Advisor/Supervisor/Committee Chair
Alexander ItsAdditional Committee Member 2
Pavel BleherAdditional Committee Member 3
Alexandre EremenkoAdditional Committee Member 4
Vitaly TarasovUsage metrics
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Keywords
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
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