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Zbl 0898.34006
Its, Alexander R.; Kapaev, Andrei A.
Connection formulae for the fourth Painlevé transcendent: Clarkson-McLeod solution. (English)
[J] J. Phys. A, Math. Gen. 31, No.17, 4073-4113 (1998). ISSN 0305-4470

Summary: Using the isomonodromy and the Riemann-Hilbert method, we perform a rigorous global asymptotic analysis of the Clarkson-McLeod fourth Painlevé transcendent. In particular, the authors prove some of the Clarkson-McLeod conjectures concerning the asymptotic behaviour, as $x\to-\infty$, of the solutions to Painlevé's fourth equation which decay as $x\to +\infty$. The relevant exact connection formulae are rigorously derived.

MSC 2000:: *34A25 Analytical theory of ODE
34A05 Methods of solution of ODE

Keywords: isomonodromy; Riemann-Hilbert method; global asymptotic analysis; Clarkson-McLeod fourth Painlevé transcendent

Cited in: Zbl 1182.33034

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