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arXiv 1601.05296math-phmath.MPmath.SGnlin.SI
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根格$Q(A_{N})$上的二维变分系统

Two-dimensional variational systems on the root lattice $Q(A_{N})$

Raphael Boll

备注：
17 pages, 3 figures. arXiv admin note: text overlap with arXiv:1506.00729
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摘要：

本文研究了根格点$Q(A_{N})$上的二维变分系统，即多拉格朗日系统。在这里，我们遵循的计划，这已经被用来定义二维多拉格朗日系统的晶格$\mathbb{Z}^{N}$和三维多拉格朗日系统的晶格$\mathbb{Z}^{N}$以及$Q(A_{N})$。我们将证明$Q(A_{N})$上的二维多拉格朗日系统比$\mathbb{Z}^{N}$上的二维多拉格朗日系统更一般，因为它们可以在$\mathbb{Z}^{N}$上编码几个不同的多拉格朗日系统。这也意味着，某些双曲型方程，所谓的四方程组的几个系统的变分公式，可以从一个和同一个多拉格朗日系统$Q(A_{N})$。

英文摘要：

We study certain two-dimensional variational systems, namely pluri-Lagrangian systems on the root lattice $Q(A_{N})$. Here, we follow the scheme which was already used to define two-dimensional pluri-Lagrangian systems on the lattice $\mathbb{Z}^{N}$ and three-dimensional pluri-Lagrangian systems on the lattice $\mathbb{Z}^{N}$ as well as on $Q(A_{N})$. We will show that the two-dimensional pluri-Lagragian systems on $Q(A_{N})$ are more general than the ones on $\mathbb{Z}^{N}$, in the sense that they can encode several different pluri-Lagrangian systems on $\mathbb{Z}^{N}$. This also means that the variational formulation of several systems of certain hyperbolic equations, so-called quad-equations, can be obtained from one and the same pluri-Lagrangian system on $Q(A_{N})$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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