Symmetry, Integrability and Geometry: Methods and Applications (Aug 2012)

Discrete Integrable Equations over Finite Fields

  • Masataka Kanki,
  • Jun Mada,
  • Tetsuji Tokihiro

Journal volume & issue
Vol. 8
p. 054

Abstract

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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