Integrable 1D Toda cellular automata

Abstract

First, we recall the algebro-geometric method of construction of finite field valued solutions of the discrete KP equation and next we perform a reduction of the dKP equation to the discrete 1D Toda equation. This gives a method of construction of solutions of the discrete 1D Toda equation taking values in a finite field.

9 pages, 2 figures; Corrected typos

References in corpus (5)

• Elliptic solutions to difference non-linear equations and related many-body problems
• Algebro-geometric solution of the discrete KP equation over a finite field out of a hyperelliptic curve
• The Hirota equation over finite fields. Algebro-geometric approach and multisoliton solutions
• The discrete KP and KdV equations over finite fields
• Integrable KP and KdV cellular automata out of a hyperelliptic curve

Cited by in corpus (2)

• On pattern structures of the N-soliton solution of the discrete KP equation over a finite field
• Superintegrable cellular automata and dual unitary gates from Yang-Baxter maps