A finite Toda representation of the box-ball system with box capacity
arXiv:1109.2266 · doi:10.1088/1751-8113/45/8/085204
Abstract
A connection between the finite ultradiscrete Toda lattice and the box-ball system is extended to the case where each box has own capacity and a carrier has a capacity parameter depending on time. In order to consider this connection, new carrier rules "size limit for solitons" and "recovery of balls", and a concept "expansion map" are introduced. A particular solution to the extended system of a special case is also presented.
20 pages, 9 figures