| Abstract: | In this paper, we discuss Airy solutions of the second Painlevé equation (PII) and two related equations, the Painlevé XXXIV equation ( ) and the Jimbo–Miwa–Okamoto σ form of PII (SII), are discussed. It is shown that solutions that depend only on the Airy function  have a completely different structure to those that involve a linear combination of the Airy functions  and  . For all three equations, the special solutions that depend only on  are tronquée solutions, i.e., they have no poles in a sector of the complex plane. Further, for both  and SII, it is shown that among these tronquée solutions there is a family of solutions that have no poles on the real axis. |
