Papers - Iwao, Shinsuke

Solutions of the generalized periodic discrete Toda equation

Shinsuke Iwao

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (IOP PUBLISHING LTD)  41 ( 11 ) 115201 2008

Accepted,  ISSN  1751-8113

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A box-ball system with more than one kind of ball is obtained by the generalized periodic discrete Toda equation (pd Toda equation). We present an algebraic geometric study of the periodic Toda equation. The time evolution of the pd Toda equation is linearized on the Picard group of an algebraic variety, and theta function solutions are obtained.

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Ultradiscretization of the theta function solution of pd Toda

Shinsuke Iwao, Tetsuji Tokihiro

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (IOP PUBLISHING LTD)  40 ( 43 ) 12987 - 13021 2007

Accepted,  ISSN  1751-8113

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

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