A delay analogue of the box and ball system (BBS) is presented. This new soliton cellular automaton is constructed by the ultra-discretization of the delay discrete Lotka–Volterra equation, which is an integrable delay analogue of the discrete Lotka–Volterra equation. Soliton patterns generated by this delay BBS are classified into normal solitons and abnormal solitons. Normal solitons have a clear relationship to the solitons of the BBS with K kinds of balls. On the other hand, abnormal solitons show various types of novel soliton patterns, which have not been observed in almost all known BBSs. We obtain them by numerical experiments, and then construct τ-functions of them analytically in 1-soliton cases.

中文翻译：

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由延迟离散 Lotka-Volterra 方程的超离散化产生的盒子和球系统的延迟模拟

提出了盒子和球系统 (BBS) 的延迟模拟。这种新的孤子元胞自动机是通过延迟离散 Lotka-Volterra 方程的超离散化构建的，它是离散 Lotka-Volterra 方程的可积延迟模拟。由该延迟BBS产生的孤子图案被分类为正常孤子和异常孤子。正常孤子与 BBS 孤子​​有明显的关系K各种球。另一方面，异常孤子表现出各种类型的新颖孤子模式，这些模式在几乎所有已知的 BBS 中都没有观察到。我们通过数值实验获得它们，然后构建τ-在 1-孤子情况下分析它们的函数。