Discrete Integrable Equations over Finite Fields - Kanki, M.; Mada, J.; Tokihiro, T. (Symmetry, Integrability and Geometry: Methods and Applications, 2012)
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.