Discrete integrable equations over finite fields

Details Discrete integrable equations over finite fields Discrete integrable equations over finite fields

2012-01-26

arxiv.org/abs/1201.5429v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

11 pages, 8 figures, v2: 13 pages, 8 figures

Scientific paper

Discrete integrable equations over finite fields are investigated. The indeterminacy of the equation is resolved by using a rational function field 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 are obtained. (v2: Relation to the singularity confinement method is discussed in the new section 4.)

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