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SIGMA, 2012, Volume 8, 054, 12 pages (Mi sigma731)  

This article is cited in 6 scientific papers (total in 6 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

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.

DOI: https://doi.org/10.3842/SIGMA.2012.054

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Full text: http://emis.mi.ras.ru/.../054
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Bibliographic databases:

ArXiv: 1201.5429
MSC: 35Q53; 37K40; 37P25
Received: May 18, 2012; in final form August 15, 2012; Published online August 18, 2012
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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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\by Masataka Kanki, Jun Mada, Tetsuji Tokihiro
\paper Discrete integrable equations over finite fields
\jour SIGMA
\yr 2012
\vol 8
\papernumber 054
\totalpages 12
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Jimenez A., “Cellular Automata to Describe Seismicity: a Review”, Acta Geophys., 61:6 (2013), 1325–1350  crossref  mathscinet  adsnasa  isi  elib  scopus
    2. Kanki M., Mada J., Tokihiro T., “The Space of Initial Conditions and the Property of an Almost Good Reduction in Discrete Painlevé II Equations Over Finite Fields”, J. Nonlinear Math. Phys., 20:1, SI (2013), 101–109  crossref  mathscinet  isi  scopus
    3. Yura F., “Solitons with a Nested Structure Over Finite Fields”, J. Phys. A-Math. Theor., 47:32 (2014), 325201  crossref  mathscinet  zmath  isi  scopus
    4. Isojima Sh., “on Exact Solutions With Periodic Structure of the Ultradiscrete Toda Equation With Parity Variables”, J. Math. Phys., 55:9 (2014), 093509  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. Bialecki M., Czechowski Z., “Random Domino Automaton: Modeling Macroscopic Properties By Means of Microscopic Rules”, Achievements, History and Challenges in Geophysics, Geoplanet-Earth and Planetary Sciences, eds. Bialik R., Majdanski M., Moskalik M., Springer-Verlag Berlin, 2014, 223–241  crossref  isi
    6. Roberts J.A.G., Tran D.T., “Signatures Over Finite Fields of Growth Properties For Lattice Equations”, J. Phys. A-Math. Theor., 48:8 (2015), 085201  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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