论文标题
长diagonal Pentagram地图
Long-diagonal pentagram maps
论文作者
论文摘要
R. Schwartz于1992年推出了投影平面中多边形的Pentagram图，到目前为止是最受欢迎和经典的离散集成系统之一。在本文中，我们介绍并证明了$ \ Mathbb {r} \ Mathrm {p}^d $的多边形上长期五角星地图的整合性，涵盖了所有已知的整合案例。我们还建立了与长diagonal和双基因图的等效性，并为这两者提供了简单的自由度结构。最后，我们证明所有这些地图的连续限制等同于$（2，d+1）$ -KDV方程，以$ d = 2 $的概括为boussinesq方程。
The pentagram map on polygons in the projective plane was introduced by R. Schwartz in 1992 and is by now one of the most popular and classical discrete integrable systems. In the present paper we introduce and prove integrability of long-diagonal pentagram maps on polygons in $\mathbb{R}\mathrm{P}^d$, encompassing all known integrable cases. We also establish an equivalence of long-diagonal and bi-diagonal maps and present a simple self-contained construction of the Lax form for both. Finally, we prove the continuous limit of all these maps is equivalent to the $ (2,d+1)$-KdV equation, generalizing the Boussinesq equation for $d=2$.
