Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 160

Connection Formulas for Asymptotics of the Fifth PainleveTranscendent on the Real Axis I

F. V. Andreev and A. V. Kitaev

This is the first part of our work in which the connection results for asymptotics as of the fifth Painleve transcendent (P_5) are collected. Keeping in mind already known and possible applications a slightly more general object is studied, that is a nonlinear system of ODEs governing isomonodromy deformations for the 2x2 matrix linear ODE ${d over dlambda} Psi = left( {tover 2} sigma_3 + {A_0over lambda}+ {A_1over lambda -1} ight) Psi .$ In this part it is considered the connection problem for the general isomonodromy deformations corresponding to solutions y(t) of P_5 such as .

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