A cellular automaton (CA) of filter automata type is proposed. Any state of the CA consists only of solitary wave solutions. It is shown that the solitary waves interact with one another preserving their identities during a time evolution. It is also shown that the CA has infinitely many conserved quantities. Hence, this CA may be considered to be one of the simplest soliton systems.

A Soliton Cellular Automaton

https://hakotama.jp/laboratory/works/public/97msttt.pdf

Toda-type cellular automaton and its N-soliton solution

Abstract We show that the cellular automaton proposed by two of the authors (D.T. and J.M.) is obtained from the discrete Toda lattice equation through a special limiting procedure. Also by applying a similar kind of limiting procedure to the N -soliton solution of the discrete Toda lattice equation, we obtain the N -soliton solution for this cellular automaton.

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Toda-type Cellular Automaton and its $N$-soliton Solution(Discretizations of Integrable Systems : Theory and Applications)

Soliton cellular automata associated with crystal bases

Combinatorial representation of invariants of a soliton cellular automaton

On etudie des automates cellulaires qui presentent un comportement soliton. On introduit le theoreme de regle rapide qui permet un calcul immediat du processus d'evolution

T. S. Papatheodorou

Papers

A Rule for Fast Computation and Analysis of Soliton Automata