Nonautonomous discrete elementary Toda orbits and their ultradiscretization

Source abstract

Abstract We derive a nonautonomous discrete analogue of the elementary Toda orbits via a spectral transformation of certain biorthogonal Laurent polynomials. We obtain particular solutions of the system by using the theory of biorthogonal polynomials. The obtained system can be written in subtraction-free form and thus can be ultradiscretized. We introduce a new family of cellular automata generalizing Takahashi and Satsuma’s box-ball system with a carrier capacity.