Box-ball systems related to the nonautonomous ultradiscrete Toda equation on the finite lattice

Abstract

Ultradiscrete analogues of the nonautonomous discrete finite Toda lattice and its modified system are explicitly given. It is shown that these two systems can be seen as the box-ball system with size limits and one with speed limits, respectively. Particular solutions and the Lax forms of these ultradiscrete systems on the finite lattice are also discussed.