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arXiv · 1203.4404

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

Shinsuke Iwao·Hidetomo Nagai·Shin Isojima
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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.

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Shinsuke Iwao, Hidetomo Nagai, Shin Isojima. 2012-03-20. Tropical Krichever construction for the non-periodic box and ball system. https://doi.org/10.1088/1751-8113%2F45%2F39%2F395202

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