Discrete Integrable Equations over Finite Fields
Exactly Solvable and Integrable Systems
2012-08-21 v3 Pattern Formation and Solitons
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.
Cite
@article{arxiv.1201.5429,
title = {Discrete Integrable Equations over Finite Fields},
author = {Masataka Kanki and Jun Mada and Tetsuji Tokihiro},
journal= {arXiv preprint arXiv:1201.5429},
year = {2012}
}