A noncommutative discrete potential KdV lift

作者：Konstantinou Rizos S^*; Kouloukas T E

来源：Journal of Mathematical Physics, 2018, 59(6): 063506.

DOI：10.1063/1.5041947

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 x 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. Published by AIP Publishing.

• 出版日期2018-6