On a Periodic Soliton Cellular Automaton

Details On a Periodic Soliton Cellular Automaton On a Periodic Soliton Cellular Automaton

2001-12-25

arxiv.org/abs/nlin/0112041v1

J. Phys. A: Math. Gen. 35, 3787 (2002).

Nonlinear Sciences

Exactly Solvable and Integrable Systems

17 pages, 5 figures

Scientific paper

10.1088/0305-4470/35/16/317

We propose a box and ball system with a periodic boundary condition (pBBS).
The time evolution rule of the pBBS is represented as a Boolean recurrence
formula, an inverse ultradiscretization of which is shown to be equivalent with
the algorithm of the calculus for the 2Nth root. The relations to the pBBS of
the combinatorial R matrix of ${U'}_q(A_N^{(1)})$ are also discussed.

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