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arXiv · 1904.06741

Connection Formulae for Asymptotics of the Fifth Painlev\'e Transcendent on the Imaginary Axis: I

F. V. Andreev·A. V. Kitaev
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Abstract

Leading terms of asymptotic expansions for the general complex solutions of the fifth Painlev\'e equation as $t\to\imath\infty$ are found. These asymptotics are parameterized by monodromy data of the associated linear ODE. $$ \frac{d}{d\lambda}Y= \left(\frac t2\sigma_3 + \frac{A_0}\lambda+\frac{A_1}{\lambda-1}\right)Y. $$ 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.

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F. V. Andreev, A. V. Kitaev. 2019-04-14. Connection Formulae for Asymptotics of the Fifth Painlev\'e Transcendent on the Imaginary Axis: I. https://arxiv.org/abs/1904.06741

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