Construction of soliton cellular automaton from the vertex model - The discrete 2D Toda equation and the Bogoyavlensky lattice

Rei Inoue, Kazuhiro Hikami

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

We study the soliton cellular automaton (SCA) in (2+1)-dimensions from the viewpoint of the integrable vertex model. As in our previous paper, we relate the SCA, the so-called box-ball system, to an integrable vertex model associated with the Bogoyavlensky lattice. We extend this framework and introduce the (2 + 1)-dimensional SCA, which can be interpreted as the ultradiscretization of the 2D Toda equation. We also construct the N-soliton solutions for this system.

Original languageEnglish
Pages (from-to)6853-6868
Number of pages16
JournalJournal of Physics A: Mathematical and General
Volume32
Issue number39
DOIs
Publication statusPublished - Oct 1 1999

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Vertex Model
cellular automata
Cellular automata
Solitons
Cellular Automata
apexes
Integrable Models
solitary waves
Soliton Solution
Ball
boxes
balls

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)

Cite this

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