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Zbl 1182.33034
Wong, R.; Zhang, H.Y.
On the connection formulas of the fourth Painlevé transcendent. (English)
[J] Anal. Appl., Singap. 7, No. 4, 419-448 (2009). ISSN 0219-5305

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.

MSC 2000:: *33E17 Painlevé-type functions
34A25 Analytical theory of ODE
34E05 Asymptotic expansions (ODE)

Keywords: uniform asymptotics; Whittaker's functions; parabolic cylinder functions

Citations: Zbl 0912.34007; Zbl 0898.34006

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