T. Tokihiro et al., Proof of solitonical nature of box and ball systems by means of inverse ultra-discretization, INVERSE PR, 15(6), 1999, pp. 1639-1662
A soliton cellular automaton, which represents movement of a finite number
of balls in an array of boxes, is investigated. Its dynamics is described b
y an ultra-discrete equation obtained from an extended Toda molecule equati
on. The rules for soliton interactions and factorization property of the sc
attering matrices (Yang-Baxter relation) are proved by means of inverse ult
ra-discretization. The conserved quantities are also presented and used for
another proof of the solitonical nature.