A geometric realization of the periodic discrete Toda lattice and its tropicalization

Atsushi Nobe*

*この研究の対応する著者

研究成果: Article査読

1 被引用数 (Scopus)

抄録

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.

本文言語English
論文番号465203
ジャーナルJournal of Physics A: Mathematical and Theoretical
46
46
DOI
出版ステータスPublished - 2013 11月 22
外部発表はい

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 統計学および確率
  • モデリングとシミュレーション
  • 数理物理学
  • 物理学および天文学(全般)

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