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From Continuous to Discrete Painlevé Equations

✍ Scribed by A.S. Fokas; B. Grammaticos; A. Ramani

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
630 KB
Volume
180
Category
Article
ISSN
0022-247X

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✦ Synopsis

Discrete analogues of the Painleve 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 nonautonomous discrete equations. These methods are based on the discrete AKNS approach, on the use of Bäcklund and Schlesinger transforms of the (continuous) Painlevé equations, and on discrete analogues of Miura transformations. ". 1993 Academic Press, Inc.

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We study the special limits of discrete Painleve´equations belonging to the qÀP VI and dÀP V families, when the independent variable goes to 1 or 0, respectively. We obtain discrete systems which are shown to be either contiguities of solutions of continuous Painleve´equations, usually of P VI but a