  Transport processes in crowded periodic structures are often mediated by
cooperative movements of particles forming clusters. Recent theoretical and
experimental studies of driven Brownian motion of hard spheres showed that
cluster-mediated transport in one-dimensional periodic potentials can proceed
in form of solitary waves. We here give a comprehensive description of these
solitons. Fundamental for our analysis is a static presoliton state, which is
formed by a periodic arrangement of basic stable clusters. Their size follows
from a geometric principle of minimum free space. Adding one particle to the
presoliton state gives rise to solitons. We derive the minimal number of
particles needed for soliton formation, number of solitons at larger particle
numbers, soliton velocities and soliton-mediated particle currents. Incomplete
relaxations of the basic clusters are responsible for an effective repulsive
soliton-soliton interaction seen in measurements. A dynamical phase transition
is predicted to occur in current-density relations at low temperatures. Our
results provide a theoretical basis for describing experiments on
cluster-mediated particle transport in periodic potentials.
