Commuting Time Evolutions in the Tropical Periodic Toda Lattice
Taichiro Takagi
TL;DR
This paper introduces a new representation for the tropical periodic Toda lattice using two-colored strips and constructs a family of commuting time evolutions, advancing the understanding of its integrable structure.
Contribution
It presents a novel formulation of the tropical periodic Toda lattice with a two-colored strip representation and develops a family of commuting time evolutions.
Findings
New two-colored strip formulation of the system
Construction of a family of commuting evolutions
Enhanced understanding of the system's integrability
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.
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