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A noncommutative discrete potential KdV lift

Konstantinou-Rizos, Sotiris, Kouloukas, Theodoros (2018) A noncommutative discrete potential KdV lift. Journal of Mathematical Physics, 59 (6). ISSN 0022-2488. (doi:10.1063/1.5041947) (KAR id:67389)

Abstract

In this paper, we construct a Grassmann extension of a Yang-Baxter map which first appeared in the work of Kouloukas and Papageorgiou [J. Phys. A: Math. Theor. 42, 404012 (2009)] and can be considered as a lift of the discrete potential Korteweg-de Vries (dpKdV) equation. This noncommutative extension satisfies the Yang-Baxter equation, and it admits a 3 × 3 Lax matrix. Moreover, we show that it can be squeezed down to a novel system of lattice equations which possesses a Lax representation and whose bosonic limit is the dpKdV equation. Finally, we consider commutative analogs of the constructed Yang-Baxter map and its associated quad-graph system, and we discuss their integrability.

Item Type: Article
DOI/Identification number: 10.1063/1.5041947
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Theodoros Kouloukas
Date Deposited: 21 Jun 2018 14:31 UTC
Last Modified: 08 Dec 2022 21:04 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/67389 (The current URI for this page, for reference purposes)

University of Kent Author Information

Kouloukas, Theodoros.

Creator's ORCID: https://orcid.org/0000-0002-9903-6788
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