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TMF, 2003, Volume 137, Number 1, Pages 66–73 (Mi tmf240)  

This article is cited in 9 scientific papers (total in 9 papers)

The Discrete KP and KdV Equations over Finite Fields

M. Bialeckia, A. Doliwab

a University of Bialystok
b Varmin'sko-Mazurskii University

Abstract: We propose an algebro-geometric method for constructing solutions of the discrete KP equation over a finite field. We also perform the corresponding reduction to the finite-field version of the discrete KdV equation. We write formulas that allow constructing multisoliton solutions of the equations starting from vacuum wave functions on an arbitrary nonsingular curve.

Keywords: integrable systems, cellular automata, finite fields

DOI: https://doi.org/10.4213/tmf240

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English version:
Theoretical and Mathematical Physics, 2003, 137:1, 1412–1418

Bibliographic databases:


Citation: M. Bialecki, A. Doliwa, “The Discrete KP and KdV Equations over Finite Fields”, TMF, 137:1 (2003), 66–73; Theoret. and Math. Phys., 137:1 (2003), 1412–1418

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Bialecki M, “Integrable 1D Toda cellular automata”, Journal of Nonlinear Mathematical Physics, 12 (2005), 28–35, Suppl. 2  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. Bialecki M, Doliwa A, “Algebro-geometric solution of the discrete KP equation over a finite field out of a hyperelliptic curve”, Communications in Mathematical Physics, 253:1 (2005), 157–170  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. Bialecki, M, “On pattern structures of the N-soliton solution of the discrete KP equation over a finite field”, Journal of Physics A-Mathematical and Theoretical, 40:5 (2007), 949  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    4. Masataka Kanki, Jun Mada, Tetsuji Tokihiro, “Discrete integrable equations over finite fields”, SIGMA, 8 (2012), 054, 12 pp.  mathnet  crossref  mathscinet
    5. Czechowski Z., Bialecki M., “Three-Level Description of the Domino Cellular Automaton”, J. Phys. A-Math. Theor., 45:15 (2012), 155101  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    6. Bialecki M., Czechowski Z., “On One-to-One Dependence of Rebound Parameters on Statistics of Clusters: Exponential and Inverse-Power Distributions Out of Random Domino Automaton”, J. Phys. Soc. Jpn., 82:1 (2013), 014003  crossref  adsnasa  isi  scopus  scopus
    7. Masataka Kanki, “Integrability of Discrete Equations Modulo a Prime”, SIGMA, 9 (2013), 056, 8 pp.  mathnet  crossref  mathscinet
    8. Yura F., “Solitons With a Nested Structure Over Finite Fields”, J. Phys. A-Math. Theor., 47:32 (2014), 325201  crossref  mathscinet  zmath  isi  scopus  scopus
    9. 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  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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