S. Konstantinou-Rizos and T.E. Kouloukas, "A noncommutative discrete potential KdV lift", Journal of Mathematical Physics, 59, 063506 (2018).

S. Konstantinou-Rizos and T.E. Kouloukas, A noncommutative discrete potential KdV lift, Journal of Mathematical Physics, 59, 063506 (2018).

https://doi.org/10.1063/1.5041947

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.

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