标题： 非交换离散位势KdV提升 显示英文标题

标题： A noncommutative discrete potential KdV lift

摘要： 在本文中，我们构建了一个Yang-Baxter映射的Grassmann扩展，该映射首次出现在[16]中，可以视为离散势Korteweg-de Vries（dpKdV）方程的提升。 这一非交换扩展满足Yang-Baxter方程，并且具有$3 \times 3$Lax矩阵。 此外，我们表明它可以压缩为一个具有Lax表示的格子方程系统，其玻色极限是dpKdV方程。 最后，我们考虑了所构造的Yang-Baxter映射及其相关四边形图系统的可交换类似物，并讨论了它们的可积性。 显示英文摘要

摘要： 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.