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On the connection formulas of the fourth Painlevé transcendent. (English) Zbl 1182.33034
Summary: Using the method of “uniform asymptotics” proposed by{\it A. P. Bassom, P. A. Clarkson, C. K. Law} and {\it J. B. McLeod} [Arch. Ration. Mech. Anal. 143, No. 3, 241--271 (1998; Zbl 0912.34007)], we provide a simpler and more rigorous proof of the connection formulas of the Clarkson-McLeod solution for the fourth Painlevé transcendent, which has been established earlier by {\it A. R. Its} and {\it A. A. Kapaev} [J. Phys. A, Math. Gen. 31, No. 17, 4073--4113 (1998; Zbl 0898.34006)] via the isomonodromy and Riemann-Hilbert methods.

33E17Painlevé-type functions
34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)
34E05Asymptotic expansions (ODE)
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