A Path-Counting Analysis of Phase Shifts in Box-Ball Systems

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2022
• ISSN: 1815-0659
• Main Authors: Ercolani, Nicholas M., Ramalheira-Tsu, Jonathan
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2022
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211724
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: A Path-Counting Analysis of Phase Shifts in Box-Ball Systems. Nicholas M. Ercolani and Jonathan Ramalheira-Tsu. SIGMA 18 (2022), 063, 42 pages

In this paper, we perform a detailed analysis of the phase shift phenomenon of the classical soliton cellular automaton known as the box-ball system, ultimately resulting in a statement and proof of a formula describing this phase shift. This phenomenon has been observed since the nineties, when the...