TY - JOUR

T1 - Box and Ball System with Numbered Boxes

AU - Yamamoto, Yusaku

AU - Fukuda, Akiko

AU - Kakizaki, Sonomi

AU - Ishiwata, Emiko

AU - Iwasaki, Masashi

AU - Nakamura, Yoshimasa

N1 - Funding Information:
The authors are grateful to the anonymous reviewer for careful reading and valuable suggestions. This research was partially supported by Grants-in-Aid for Scientific Research (C) No. 19K03624 from the Japan Society for the Promotion of Science.
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature B.V.

PY - 2022/6

Y1 - 2022/6

N2 - The box and ball system (BBS) models the dynamics of balls moving among an array of boxes. The simplest BBS is derived from the ultradiscretization of the discrete Toda equation, which is one of the most famous discrete integrable systems. The discrete Toda equation can be extended to two types of discrete hungry Toda (dhToda) equations, one of which is the equation of motion of the BBS with numbered balls (nBBS). In this paper, based on the ultradiscretization of the other type of dhToda equation, we present a new nBBS in which not balls, but boxes, are numbered. We also investigate conserved quantities with respect to balls and boxes, the solitonical nature of ball motions, and a scattering rule in collisions of balls to clarify the characteristics of the resulting nBBS.

AB - The box and ball system (BBS) models the dynamics of balls moving among an array of boxes. The simplest BBS is derived from the ultradiscretization of the discrete Toda equation, which is one of the most famous discrete integrable systems. The discrete Toda equation can be extended to two types of discrete hungry Toda (dhToda) equations, one of which is the equation of motion of the BBS with numbered balls (nBBS). In this paper, based on the ultradiscretization of the other type of dhToda equation, we present a new nBBS in which not balls, but boxes, are numbered. We also investigate conserved quantities with respect to balls and boxes, the solitonical nature of ball motions, and a scattering rule in collisions of balls to clarify the characteristics of the resulting nBBS.

KW - Box and ball system

KW - Discrete hungry Toda equation

KW - Numbered boxes

KW - Solitonical nature

KW - Ultradiscretization

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U2 - 10.1007/s11040-022-09425-6

DO - 10.1007/s11040-022-09425-6

M3 - Article

AN - SCOPUS:85128863605

VL - 25

JO - Mathematical Physics Analysis and Geometry

JF - Mathematical Physics Analysis and Geometry

SN - 1385-0172

IS - 2

M1 - 13

ER -