Ultradiscretization of the solution of periodic Toda equation

Abstract

A periodic box-ball system (pBBS) is obtained by ultradiscretizing the periodic discrete Toda equation (pd Toda eq.). We show the relation between a Young diagram of the pBBS and a spectral curve of the pd Toda eq.. The formula for the fundamental cycle of the pBBS is obtained as a colloraly.

arXiv comment41 pages; 7 figures

References in corpus (3)

• Fundamental Cycle of a Periodic Box-Ball System
• Simple strong glass forming models: mean-field solution with activation
• When is negativity not a problem for the ultra-discrete limit?

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