Discrete Integrable Equations over Finite Fields

Symmetry Integrability and Geometry-Methods and Applications

article

Masataka Kanki¹  Jun Mada²  Tetsuji Tokihiro¹ 

[1] Graduate School of Mathematical Sciences, University of Tokyo;College of Industrial Technology, Nihon University

关键词: integrable system;    discrete KdV equation;    finite field;    cellular automaton;   

DOI  :  10.3842/SIGMA.2012.054

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown