Tropical curves and integrable piecewise linear maps
Rei Inoue, Shinsuke Iwao
TL;DR
This paper explores how tropical geometry can be applied to analyze integrable piecewise-linear maps, specifically focusing on spectral curves and isolevel sets of certain systems, providing new insights and results in the field.
Contribution
It introduces novel applications of tropical geometry to integrable systems, including analysis of spectral curves and isolevel sets for tropical periodic Toda lattice and Box-ball system.
Findings
Analysis of spectral curves for tropical systems
Description of isolevel sets in tropical integrable maps
New results on tropical periodic Toda lattice
Abstract
We present applications of tropical geometry to some integrable piecewise-linear maps, based on the lecture given by one of the authors (R. I.) at the workshop "Tropical Geometry and Integrable Systems" (University of Glasgow, July 2011), and on some new results obtained afterward. After a brief review on tropical curve theory, we study the spectral curves and the isolevel sets of the tropical periodic Toda lattice and the periodic Box-ball system.
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Taxonomy
TopicsNonlinear Waves and Solitons · Polynomial and algebraic computation · Advanced Differential Equations and Dynamical Systems