论文标题
扩展的晶格Gelfand-Dickey层次结构
Extended lattice Gelfand-Dickey hierarchy
论文作者
论文摘要
晶格Gelfand-Dickey层次结构是Gelfand-Dickey层次结构的晶格版本。特殊情况是晶格KDV层次结构。受Buryak和Rossi的最新作品的启发，我们提出了晶格Gelfand-Dickey层次结构的扩展。扩展系统在通常的流动旁边具有无限数量的对数流。我们提出了宽松的，佐藤和海洛塔方程，以及捕获整个解决方案集的差异操作员的分解问题。该系统的构建类似于扩展的1D和Bigraded Toda层次结构，但也表现出了一些新颖的功能。
The lattice Gelfand-Dickey hierarchy is a lattice version of the Gelfand-Dickey hierarchy. A special case is the lattice KdV hierarchy. Inspired by recent work of Buryak and Rossi, we propose an extension of the lattice Gelfand-Dickey hierarchy. The extended system has an infinite number of logarithmic flows alongside the usual flows. We present the Lax, Sato and Hirota equations and a factorization problem of difference operators that captures the whole set of solutions. The construction of this system resembles the extended 1D and bigraded Toda hierarchy, but exhibits several novel features as well.
