Connection Formulae for Asymptotics of the Fifth Painlevé Transcendent on the Imaginary Axis: I

Abstract

Leading terms of asymptotic expansions for the general complex solutions of the fifth Painlevé equation as $t\to ı\infty$ are found. These asymptotics are parameterized by monodromy data of the associated linear ODE. $$\frac{d}{d\lambda }Y=\left(\frac{t}{2}{\sigma }_3+\frac{A_0}{\lambda }+\frac{A_1}{\lambda -1}\right)Y.$$ The parametrization allows one to derive connection formulas for the asymptotics. We provide numerical verification of the results. Important special cases of the connection formulas are also considered.

71 pages, 30 figures

References in corpus (1)

• Irregular conformal blocks and connection formulae for Painlevé V functions