Discrete Integrable Equations over Finite Fields

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.

References in corpus (2)

• Yang-Baxter maps and symmetries of integrable equations on quad-graphs
• On pattern structures of the N-soliton solution of the discrete KP equation over a finite field

Cited by in corpus (4)

• Discrete Painleve II equation over finite fields
• Solitons with nested structure over finite fields
• The space of initial conditions and the property of an almost good reduction in discrete Painleve II equations over finite fields
• Superintegrable cellular automata and dual unitary gates from Yang-Baxter maps