Tropical Krichever construction for the non-periodic box and ball system

TL;DR

This paper introduces a tropical geometry-based method to construct solutions for the non-periodic box and ball system by limiting from the periodic case, providing an algebro-geometric approach to integrable systems.

Contribution

It develops a tropical analogue of the Krichever construction for non-periodic systems, extending integrable systems theory.

Findings

Constructed solutions for the non-periodic box and ball system.

Established a limiting process from periodic to non-periodic systems.

Connected tropical geometry with integrable systems theory.

Abstract

A solution for an initial value problem of the box and ball system is constructed from a solution of the periodic box and ball system. The construction is done through a specific limiting process based on the theory of tropical geometry. This method gives a tropical analogue of the Krichever construction, which is an algebro-geometric method to construct exact solutions to integrable systems, for the non-periodic system.