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A delay analogue of the box and ball system (BBS) is presented. This newsoliton cellular automaton is constructed by the ultra-discretization of thedelay discrete Lotka-Volterra equation, which is an integrable delay analogueof the discrete Lotka-Volterra equation. Soliton patterns generated by thisdelay BBS are classified into normal solitons and abnormal solitons. Normalsolitons have a clear relationship to the solitons of the BBS with K kinds ofballs. On the other hand, abnormal solitons show various types of novel solitonpatterns, which have not been observed in almost all known BBSs. We obtain themby numerical experiments, and then construct {\tau}-functions of themanalytically in 1-soliton cases.

A delay analogue of the box and ball system arising from the ultra-discretization of the delay discrete Lotka-Volterra equation