The Bethe ansatz in a periodic box-ball system and the ultradiscrete Riemann theta function

Abstract

Vertex models with quantum group symmetry give rise to integrable cellular automata at q=0. We study a prototype example known as the periodic box-ball system. The initial value problem is solved in terms of an ultradiscrete analogue of the Riemann theta function whose period matrix originates in the Bethe ansatz at q=0.

11 pages, 1 figure

References in corpus (1)

• Bethe ansatz and inverse scattering transform in a periodic box-ball system

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