Combinatorial aspects of the conserved quantities of the tropical periodic Toda lattice
type: Item
instance of: scholarly article
title: Combinatorial aspects of the conserved quantities of the tropical periodic Toda lattice
zbMATH Open document ID: 1301.37050
DOI: 10.1088/1751-8113/47/39/395201
author: Taichiro Takagi
published in: Journal of Physics A: Mathematical and Theoretical
publication date: 2014-10-20T00:00:00Z
full work available at URL: https://arxiv.org/abs/1401.3395
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 37K60
zbMATH DE Number: 6359161
zbMATH Keywords: Toda lattice
zbMATH Keywords: tropical geometry
zbMATH Keywords: integrable system
zbMATH Keywords: soliton
zbMATH Keywords: Young diagram
MaRDI profile type: Publication
OpenAlex ID: W2054902745
arXiv ID: 1401.3395
review text: The Toda lattice, an integrable system with potential chosen to exhibit solitons, has an analogous system in the setting of tropical geometry. There are choices of how to define the system and here it is shown that the Young diagram (analogous to soliton solutions) associated to the system, which is easily seen to be preserved under time evolution in the construction using the Lax representation as the discrete periodic Toda lattice, is also preserved under time evolution in the system constructed using a generalization of the Kerov-Kirillov-Reshetikhin bijection for the Bethe ansatz [\textit{S. V. Kerov} et al., J. Sov. Math. 41, No. 2, 916--924 (1988; Zbl 0639.20028)]. The paper also discusses the significance of the tropical model for the more general developments in tropical geometry and integrable systems.
reviewed by: Thomas B. Ward
description: scientific article; zbMATH DE number 6359161