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The box-ball system (BBS) is a cellular automaton that is an ultradiscreteanalogue of the Korteweg--de Vries equation, a non-linear PDE used to modelwater waves. In 2001, Hikami and Inoue generalised the BBS to the generallinear Lie superalgebra $\mathfrak{gl}(m|n)$. We further generalise theHikami--Inoue BBS to column tableaux using the Kirillov--Reshetikhin crystalsfor $\hat{\mathfrak{gl}}{(m|n)}$ devised by Kwon and Okado (arXiv:1804.05456),where we find similar solitonic behaviour under certain conditions.

Soliton cellular automata for the affine general linear Lie superalgebra