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ZN graded discrete Lax pairs and Yang–Baxter maps

Fordy, Allan P., Xenitidis, Pavlos (2017) ZN graded discrete Lax pairs and Yang–Baxter maps. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 473 (2201). p. 20160946. ISSN 1364-5021. (doi:10.1098/rspa.2016.0946) (KAR id:62291)

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We recently introduced a class of ZNZN graded discrete Lax pairs and studied the associated discrete integrable systems (lattice equations). In this paper, we introduce the corresponding Yang–Baxter maps. Many well-known examples belong to this scheme for N=2, so, for N?3, our systems may be regarded as generalizations of these. In particular, for each N we introduce a class of multi-component Yang–Baxter maps, which include HBIII (of Papageorgiou et al. 2010 SIGMA 6, 003 (9 p). (doi:10.3842/SIGMA.2010.033)), when N=2, and that associated with the discrete modified Boussinesq equation, for N=3. For N?5 we introduce a new family of Yang–Baxter maps, which have no lower dimensional analogue. We also present new multi-component versions of the Yang–Baxter maps FIV and FV (given in the classification of Adler et al. 2004 Commun. Anal. Geom. 12, 967–1007. (doi:10.4310/CAG.2004.v12.n5.a1)).

Item Type: Article
DOI/Identification number: 10.1098/rspa.2016.0946
Uncontrolled keywords: discrete integrable system, Lax pair, symmetry, Yang–Baxter map
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Pavlos Xenitidis
Date Deposited: 14 Jul 2017 11:59 UTC
Last Modified: 16 Feb 2021 13:46 UTC
Resource URI: (The current URI for this page, for reference purposes)
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