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

Author:

Kenta Nakata, Kanta Negishi, Hiroshi Matsuoka, Ken-ichi Maruno

Keyword:

Nonlinear Sciences, Exactly Solvable and Integrable Systems, Exactly Solvable and Integrable Systems (nlin.SI), Mathematical Physics (math-ph)

journal:

date:

2023-09-01 16:00:00

Abstract

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. This delay BBS requires multiple time initial states for time evolution, thus it has various types of soliton patterns. Soliton patterns generated by the delay BBS are classified into normal solitons and abnormal solitons. Normal solitons can be discussed analytically, while abnormal solitons show various phenomena which are not explained easily. Finally, we show that the delay BBS is equivalent to the BBS with K kinds of balls if we consider only normal solitons.

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