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Ultradiscrete Systems (Cellular Automata)

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Discrete Integrable Systems

Part of the book series: Lecture Notes in Physics ((LNP,volume 644))

Abstract

Ultradiscretization is a limiting procedure which allows one to obtain a cellular automaton (CA) from continuous equations. Using this method, we can construct integrable CAs from integrable partial difference equations. In this course, we focus on a typical integrable CA, called a Box and Ball system (BBS), and review its peculiar features. Since a BBS is an ultradiscrete limit of the discrete KP equation and discrete Toda equation, we can obtain explicit solutions and conserved quantities for the BBS. Furthermore the BBS is also regarded as a limit (crystallization) of an integrable lattice model. Recent topics, and a periodic BBS in particular are also reviewed.

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Authors and Affiliations

  1. Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan

    Tetsuji Tokihiro

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  1. Tetsuji Tokihiro
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Basil Grammaticos Thamizharasi Tamizhmani Yvette Kosmann-Schwarzbach

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Tokihiro, T. Ultradiscrete Systems (Cellular Automata). In: Grammaticos, B., Tamizhmani, T., Kosmann-Schwarzbach, Y. (eds) Discrete Integrable Systems. Lecture Notes in Physics, vol 644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40357-9_9

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  • DOI: https://doi.org/10.1007/978-3-540-40357-9_9

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  • Print ISBN: 978-3-540-21425-0

  • Online ISBN: 978-3-540-40357-9

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