  Using the whurl relation of the first two authors, we define a new discrete
solitonic system, which we call the box-basket-ball system, generalizing the
box-ball system of Takahashi and Satsuma. In box-basket-ball systems balls may
be put either into boxes or into baskets. While boxes stay fixed, both balls
and baskets get moved during time evolution. Balls and baskets behave as
fermionic and bosonic particles respectively. We classify the solitons of this
system, and study their scattering.
