A geometric realization of the periodic discrete Toda lattice and its tropicalization
A geometric realization of the periodic discrete Toda lattice and its tropicalization
复制标题
周期性离散Toda晶格的几何实现及其热带化
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Atsushi Nobe
中科院分区：
文献类型：
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作者：
Atsushi Nobe
给出了曲线交点等价于周期离散Toda格子(PdTL)的时间演化的显式公式。首先将时间演化实现为一条超椭圆曲线上的点加运算，这是pdTL的频谱曲线，然后将该点加运算转化为曲线交点。其次，利用pdTL的守恒量，显式地给出了曲线交点上的曲线。最后，将该公式提升到热带几何的框架下，通过热带曲线交点构造了周期箱球系统的热带几何实现。
An explicit formula concerning curve intersections equivalent to the time evolution of the periodic discrete Toda lattice (pdTL) is presented. First, the time evolution is realized as a point addition on a hyperelliptic curve, which is the spectral curve of the pdTL, then the point addition is translated into curve intersections. Next, it is shown that the curves which appear in the curve intersections are explicitly given by using the conserved quantities of the pdTL. Finally, the formulation is lifted to the framework of tropical geometry and a tropical geometric realization of the periodic box–ball system is constructed via tropical curve intersections.
热带几何和可积系统
DOI：
10.1090/conm/580/11499
发表时间：
2012
期刊：
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影响因子：
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作者：
Block F
通讯作者：
Block F