Abstract
In this paper, we prove the one-soliton solutions to the solitonic dynamical system over finite fields that may be regarded as an analogue of the box-ball systems. It turns out that the one-soliton solution has a nested structure similar to fractals, and as far as we know such a system seems to be novel. Furthermore, in spite of such a complex internal structure, numerical simulations show stable propagations before and after collisions among multiple solitons with preserving their patterns.
