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SIGMA 2 (2006), 005, 11 pages nlin.SI/0507004
https://doi.org/10.3842/SIGMA.2006.005
Integrable Discrete Equations Derived by Similarity Reduction of the Extended Discrete KP Hierarchy
Andrei K. Svinin
Institute for System Dynamics and Control Theory, 134 Lermontova Str., P.O. Box 1233, Irkutsk, 664033 Russia
Received November 16, 2005, in final form January 08, 2006; Published online January 19, 2006
Abstract
We consider the extended discrete KP hierarchy and show
that similarity reduction of its subhierarchies lead to purely
discrete equations with dependence on some number of parameters
together with equations governing deformations with respect to
these parameters. It is written down discrete equations which
naturally generalize the first discrete Painlevé equation
dPI in a sense that autonomous version of these
equations admit the limit to the first Painlevé equation. It is
shown that each of these equations describes Bäcklund
transformations of Veselov-Shabat periodic dressing lattices with
odd period known also as Noumi-Yamada systems of type
A2(n-1)(1).
Key words:
extended discrete KP hierarchy; similarity reductions; discrete Painlevé equations.
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