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We experimentally study the dynamics of weakly interacting Bose-Einsteincondensates of cesium atoms in a 1D optical lattice with a periodic drivingforce. After a sudden start of the driving we observe the formation of stablewave packets at the center of the first Brillouin zone (BZ) in momentum space,and we interpret these as Floquet solitons in periodically driven systems. Thewave packets become unstable when we add a trapping potential along the latticedirection leading to a redistribution of atoms within the BZ. The concept of anegative effective mass and the resulting changes to the interaction strengthand effective trapping potential are used to explain the stability and the timeevolution of the wave packets. We expect that similar states of matter wavesexist for discrete breathers and other types of lattice solitons inperiodically driven systems.

Floquet solitons and dynamics of periodically driven matter waves with negative effective mass