Phys. Rev. Lett. 67, 1829–1832 (1991)Discrete versions of the Painlevé equationsReceived 10 April 1991; published in the issue dated 30 September 1991 We present discrete forms of the Painlevé transcendental equations PIII, PIV, and PV that complement the list of the already known PI and PII. These, most likely integrable, nonautonomous mappings go over to the usual Painlevé equations in the continuous limit, while in the autonomous limit we recover discrete system that belong to the integrable family of Quispel et al. Finally, we show that the discrete Painlevé mappings satisfy the same reduction relations as the continuous Painlevé transcendents, namely, PV→{PIII, PIV}→PII→PI. © 1991 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.67.1829
DOI:
10.1103/PhysRevLett.67.1829
PACS:
05.50.+q, 02.90.+p
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