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Zbl 0794.34013
Fokas, A.S.; Grammaticos, B.; Ramani, A.
From continuous to discrete Painlevé equations. (English)
[J] J. Math. Anal. Appl. 180, No.2, 342-360 (1993). ISSN 0022-247X

Summary: Discrete analogues of the Painlevé equations have recently been derived using either a method based on orthogonal polynomials or the singularity confinement method. Here we analyze additional methods for deriving integrable non-autonomous discrete equations. These methods are based on the discrete AKNS approach, on the use of Bäcklund und Schlesinger transforms of the (continuous) Painlevé equations, and on discrete analogues of Miura transformations.

MSC 2000:: *34A25 Analytical theory of ODE
81Q05 Closed and approximate solutions to quantum-mechanical equations
39A10 Difference equations

Keywords: discrete analogues of the Painlevé equations; integrable non-autonomous discrete equations; discrete AKNS approach; Bäcklund und Schlesinger transforms; Miura transformations

Cited in: Zbl 1056.34102

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