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arXiv · 1307.5208

Twisted reductions of integrable lattice equations, and their Lax representations

Christopher M. Ormerod·Peter H. van der Kamp·Jarmo Hietarinta·G. R. W. Quispel
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Abstract

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 equation, discrete modified Korteweg-de Vries equation and the discrete Schwarzian Korteweg-de Vries equation. We will also describe a direct method for obtaining Lax representations for the reduced equations.

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Christopher M. Ormerod, Peter H. van der Kamp, Jarmo Hietarinta, G. R. W. Quispel. 2014-04-02. Twisted reductions of integrable lattice equations, and their Lax representations. https://doi.org/10.1088/0951-7715%2F27%2F6%2F1367

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