Symmetry methods for difference equations on non-rectangular lattices.

非矩形晶格上差分方程的对称方法。

• 批准号: 2289907
• 金额: --
• 依托单位: University of Kent
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2289907
• 关键词: Symmetry; methods; difference; equations; non

The development of symmetry methods for general difference equations is still in its infancy. Although a substantial amount is known about difference equations on rectangular lattices, relatively little has been proved in the case where the underlying lattice is not rectangular (for instance, where using a moving frame creates holes in the lattice of difference invariants). The purpose of this project is to begin to address this problem, using recently-discovered results on moving frames and lattice varieties. The project will begin by generalising the difference moving frame construction to multiple independent variables, which should yield the first group-invariant Noether-type theorems for partial difference equations. Likely future directions include exploiting solvability in the moving frame construction and creating global difference structures on lattice varieties

一般差异方程的对称方法的发展仍处于起步阶段。尽管有关矩形晶格的差异方程的大量已知，但在基础晶格不是矩形的情况下，相对较少的证明（例如，使用移动框架在差异不变的晶格中产生孔洞）。该项目的目的是使用最近发现的移动框架和格子品种的结果开始解决此问题。该项目将首先将差异框架构造概括为多个独立变量，该变量应为部分差异方程提供第一个组不变的Noether-Noether-type定理。未来可能的方向包括在移动框架构造中利用可溶性以及在晶格品种上创建全球差异结构