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Connection Problem for Painlevé tau Functions

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thesis
posted on 16.10.2019, 16:19 by Andrei 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.

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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History

Degree Type

Doctor of Philosophy

Department

Mathematics

Campus location

Indianapolis

Advisor/Supervisor/Committee Chair

Alexander Its

Additional Committee Member 2

Pavel Bleher

Additional Committee Member 3

Alexandre Eremenko

Additional Committee Member 4

Vitaly Tarasov

Licence

Exports