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.
Transactions of the Japan Society for Industrial and Applied Mathematics 24 (4), 317-336, 2014
The Japan Society for Industrial and Applied Mathematics