Twisted reductions of integrable lattice equations, and their Lax representations

It is well known that from two-dimensional lattice equations one can derive one-dimensional lattice equations by imposing periodicity in some direction. In this paper we generalize the periodicity condition by adding a symmetry transformation and apply this idea to autonomous and non-autonomous latt...

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Bibliographic Details
Published in:Nonlinearity 2014-06, Vol.27 (6), p.1367-1390
Main Authors: Ormerod, Christopher M, van der Kamp, Peter H, Hietarinta, Jarmo, Quispel, G R W
Format: Article
Language:English
Subjects:
discrete Painleve
integrable
lattice equations
Lattices
Mathematical analysis
Nonlinearity
Reduction
reductions
Representations
Symmetry
Transformations
Two dimensional
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Summary:It is well known that from two-dimensional lattice equations one can derive one-dimensional lattice equations by imposing periodicity in some direction. In this paper we generalize the periodicity condition by adding a symmetry transformation and apply this idea to autonomous and non-autonomous lattice equations. As results of this approach, we obtain new reductions of the discrete potential Korteweg-de Vries (KdV) equation, discrete modified KdV equation and the discrete Schwarzian KdV equation. We will also describe a direct method for obtaining Lax representations for the reduced equations.
ISSN:0951-7715
1361-6544
DOI:10.1088/0951-7715/27/6/1367