ℤ_N graded discrete Lax pairs and Yang-Baxter maps

2015/10/19 by Fordy, Allan P., Xenitidis, Pavlos
#37K10 #37P05 #39A20 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1510.05590

Abstract

We recently introduced a class of ℤ_N 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 generalisations of these. In particular, for each N we introduce a generalisation of the map H_III^B in the classification of scalar Yang-Baxter maps. For N=3 this is equivalent to the Yang-Baxter map associated with the discrete modified Boussinesq equation. For N≥ 5 (and odd) we introduce a new family of Yang-Baxter maps, which have no lower dimensional analogue. We also present multi-component versions of the Yang-Baxter maps F_IV and F_V (given in the ABS classification).

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