Summary: Using the method of “uniform asymptotics” proposed byA. P. Bassom, P. A. Clarkson, C. K. Law
and 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 A. R. Its
and A. A. Kapaev
[J. Phys. A, Math. Gen. 31, No. 17, 4073–4113 (1998; Zbl 0898.34006
)] via the isomonodromy and Riemann-Hilbert methods.