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Symmetry, Integrability and Geometry: Methods and Applications, 2012, Volume 8, 054, 12 pp.
DOI: https://doi.org/10.3842/SIGMA.2012.054 (Mi sigma731) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Discrete integrable equations over finite fields

Masataka Kankia, Jun Madab, Tetsuji Tokihiroa

a Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Tokyo 153-8914, Japan
b College of Industrial Technology, Nihon University, 2-11-1 Shin-ei, Narashino, Chiba 275-8576, Japan
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DOI: https://doi.org/10.3842/SIGMA.2012.054
Abstract: Discrete integrable equations over finite fields are investigated. The indeterminacy of the equation is resolved by treating it over a field of rational functions instead of the finite field itself. The main discussion concerns a generalized discrete KdV equation related to a Yang–Baxter map. Explicit forms of soliton solutions and their periods over finite fields are obtained. Relation to the singularity confinement method is also discussed.
Keywords: integrable system, discrete KdV equation, finite field, cellular automaton.
Received: May 18, 2012; in final form August 15, 2012; Published online August 18, 2012
Bibliographic databases:
Document Type: Article
MSC: 35Q53; 37K40; 37P25
Language: English
Citation: Masataka Kanki, Jun Mada, Tetsuji Tokihiro, “Discrete integrable equations over finite fields”, SIGMA, 8 (2012), 054, 12 pp.
Citation in format AMSBIB
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\paper Discrete integrable equations over finite fields
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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