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Published June 2014 | Submitted
Journal Article Open

Twisted reductions of integrable lattice equations, and their Lax representations

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 (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.

Additional Information

© 2014 2014 IOP Publishing Ltd & London Mathematical Society. Received 19 July 2013, revised 10 April 2014. Accepted for publication 11 April 2014. Published 16 May 2014. Paper Recommended by T Grava. The authors are grateful to Dr V Mangazeev for a question posed at the ANZAMP Inaugural Meeting in Lorne, December 2012, that led to this paper being written. They would also like to thank Dr B Grammaticos for some references on discrete Painlevé equations. This research is supported by Australian Research Council Discovery Grants #DP110100077 and #DP140100383.

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August 20, 2023
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