2022/07/17 by Atsushi Maeno, Maeno, Atsushi, Satoshi Tsujimoto +1
Physics and Astronomy · Computer Science · Economics, Econometrics and Finance · #Chaos control and synchronization #Nonlinear Dynamics and Pattern Formation #Complex Systems and Time Series Analysis
paper · pdf · doi:10.48550/arxiv.2207.08066
We construct a bijection between the state of the box-ball system with box capacity L and a pair of two sequences. In time evolution, one of the sequences moves at speed 1, and the other follows the rules of the box-ball system with box capacity one, which can be linearized by the Kerov-Kirillov-Reshetikhin(KKR) bijection. Our method can be applied to a state including a negative value or a value greater than the box capacity.