  We experimentally study the dynamics of weakly interacting Bose-Einstein
condensates of cesium atoms in a 1D optical lattice with a periodic driving
force. After a sudden start of the driving we observe the formation of stable
wave packets at the center of the first Brillouin zone (BZ) in momentum space,
and we interpret these as Floquet solitons in periodically driven systems. The
wave packets become unstable when we add a trapping potential along the lattice
direction leading to a redistribution of atoms within the BZ. The concept of a
negative effective mass and the resulting changes to the interaction strength
and effective trapping potential are used to explain the stability and the time
evolution of the wave packets. We expect that similar states of matter waves
exist for discrete breathers and other types of lattice solitons in
periodically driven systems.
