Another generalization of the box–ball system with many kinds of balls. Issue 1 (6th June 2018)

• Record Type: Journal Article
• Authors: Maeda, Kazuki
• Is Part Of: Journal of integrable systems. Volume 3:Issue 1(2018)
• Publication Date: 2018-06-06
• Subjects: box–ball systems -- non-autonomous discrete two-dimensional Toda lattice -- biorthogonal polynomials -- spectral transformations; Mathematics -- Periodicals; 510
• DOI: 10.1093/integr/xyy007
• Languages: English
• ISSNs: 2058-5985

Abstract

Abstract: A cellular automaton that is a generalization of the box–ball system with either many kinds of balls or finite carrier capacity is proposed and studied through two discrete integrable systems: non-autonomous discrete KP lattice and non-autonomous discrete two-dimensional Toda lattice. Applying reduction technique and ultradiscretization procedure to these discrete systems, we derive two types of time evolution equations of the proposed cellular automaton, and particular solutions to the ultradiscrete equations. Communicated by: Rei Inoue Yamazaki