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arXiv · 1611.08923

A noncommutative discrete potential KdV lift

Sotiris Konstantinou-Rizos·Theodoros E. Kouloukas
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Abstract

In this paper, we construct a Grassmann extension of a Yang-Baxter map which first appeared in [16] 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 $3 \times 3$ Lax matrix. Moreover, we show that it can be squeezed down to a system of lattice equations which possesses a Lax representation and whose bosonic limit is the dpKdV equation. Finally, we consider commutative analogues of the constructed Yang-Baxter map and its associated quad-graph system, and we discuss their integrability.

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Sotiris Konstantinou-Rizos, Theodoros E. Kouloukas. 2016-11-27. A noncommutative discrete potential KdV lift. https://doi.org/10.1063/1.5041947

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