Prokhorov, Andrei
Connection Problem for PainlevĂ© tau Functions
<div>We derive the differential identities for isomonodromic tau functions, describing their monodromy dependence. </div><div> 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. </div><div> We use these identities to solve the connection problem for generic solution of Painlev\'e-III(D8) equation, and homogeneous Painlev\'e-II equation. </div><div> </div><div> 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.</div>
Painlev\'e equations;isomonodromic tau function;connection problem;Hamiltonian systems;classical action;quasihomogeneous function;Riemann-Hilbert correspondence;isomonodromic deformations
2019-10-16
https://hammer.figshare.com/articles/thesis/Connection_Problem_for_Painlev_tau_Functions/8847938

10.25394/PGS.8847938.v1