Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 2 (2006), 005, 11 pages      nlin.SI/0507004      http://dx.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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