Commuting Time Evolutions in the Tropical Periodic Toda Lattice

Abstract

The tropical (ultradiscrete) periodic Toda lattice is a dynamical system derived from a time-discretized version of the periodic Toda lattice through a limiting procedure called tropicalization. We propose a new formulation for this dynamical system with a representation by two-colored strips. Based on this formulation, a family of its commuting time evolutions is constructed.

16 pages

References in corpus (3)

• Bethe ansatz and inverse scattering transform in a periodic box-ball system
• Ultradiscretization of the solution of periodic Toda equation
• Fermionic partition functions for a periodic soliton cellular automaton