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

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Abstract

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.

Original languageEnglish
Article number465203
JournalJournal of Physics A: Mathematical and Theoretical
Volume46
Issue number46
DOIs
Publication statusPublished - 2013 Nov 22
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

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