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Connection formulae for asymptotics of the fifth Painlevé transcendent on the imaginary axis: I
Author(s) -
Andreev Fedor V.,
Kitaev Alexander V.
Publication year - 2020
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12323
Subject(s) - connection (principal bundle) , mathematics , ode , parameterized complexity , monodromy , mathematical analysis , pure mathematics , geometry , combinatorics
Leading terms of asymptotic expansions for the general complex solutions of the fifth Painlevé equation as t → ı ∞ are found. These asymptotics are parameterized by monodromy data of the associated linear ODE,d d λ Y = t 2 σ 3 + A 0 λ + A 1 λ − 1Y . The parameterization allows one to derive connection formulae for the asymptotics. We provide numerical verification of the results. Important special cases of the connection formulae are also considered.