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This article is cited in 13 scientific papers (total in 13 papers)
On the relation between the continuous and discrete Painlevé equations
P. A. Clarkson, E. L. Mansfield, H. N. Webster University of Kent
Abstract:
A method for deriving difference equations (the discrete Painlevé equations in particular) from the Bäcklund transformations of the continuous Painlevé equations is discussed. This technique can be used to derive several of the known discrete Painlevé equations (in particular, the first and second discrete Painlevé equations and some of their alternative versions). The Painlevé equations possess hierarchies of rational solutions and one-parameter families of solutions expressible in terms of the classical special functions for special values of the parameters. Hence, the aforementioned relations can be used to generate hierarchies of exact solutions for the associated discrete Painlevé equations. Exact solutions of the Painlevé equations simultaneously satisfy both a differential equation and a difference equation, analogously to the special functions.
Citation:
P. A. Clarkson, E. L. Mansfield, H. N. Webster, “On the relation between the continuous and discrete Painlevé equations”, TMF, 122:1 (2000), 5–22; Theoret. and Math. Phys., 122:1 (2000), 1–16
Linking options:
https://www.mathnet.ru/eng/tmf551https://doi.org/10.4213/tmf551 https://www.mathnet.ru/eng/tmf/v122/i1/p5
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Abstract page: | 463 | Full-text PDF : | 212 | References: | 53 | First page: | 1 |
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