Nonautonomous ultradiscrete hungry Toda lattice and a generalized box ball system
A nonautonomous version of the ultradiscrete hungry Toda lattice with a finite lattice boundary condition is derived by applying reduction and ultradiscretization to a nonautonomous two dimensional discrete Toda lattice. It is shown that the derived ultradiscrete system has a direct connection to the box ball system with many kinds of balls and finite carrier capacity. Particular solutions to the ultradiscrete system are constructed by using the theory of some sort of discrete biorthogonal polynomials.