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On Airy Solutions of the Second Painleve Equation

Clarkson, Peter (2016) On Airy Solutions of the Second Painleve Equation. Studies in Applied Mathematics, 137 (1). pp. 93-109. ISSN 0022-2526. (doi:10.1111/sapm.12123) (KAR id:51255)


In this paper, we discuss Airy solutions of the second Painleve equation and two related equations, the Painleve XXXIV equation and the Jimbo-Miwa-Okamoto sigma form of second Painleve equation, are discussed. It is shown that solutions which depend only on the Airy function Ai(z) have a completely difference structure to those which involve a linear combination of the Airy functions Ai(z) and Bi(z). For all three equations, the special solutions that depend only on inline image are tronquée solutions, i.e., they have no poles in a sector of the complex plane. Further, for both inline image and SII, it is shown that among these tronquée solutions there is a family of solutions that have no poles on the real axis.

Item Type: Article
DOI/Identification number: 10.1111/sapm.12123
Subjects: Q Science > QA Mathematics (inc Computing science) > QA351 Special functions
Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Peter Clarkson
Date Deposited: 29 Oct 2015 09:16 UTC
Last Modified: 08 Dec 2022 23:32 UTC
Resource URI: (The current URI for this page, for reference purposes)

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