  We study super Bloch oscillations of ultracold atoms in a shaken lattice
potential, subjected to a harmonically modulated mean-field interaction.
Usually, any interaction leads to the decay of the wave packet and its super
Bloch oscillation. Here, we use the phases of interaction and shaking with
respect to the free Bloch oscillation as control parameters. We find two types
of long-living cases: (i) suppression of the immediate broadening of the wave
packet, and (ii) dynamical stability of all degrees of freedom. The latter
relies on the rather robust symmetry argument of cyclic time [Gaul et al.,
Phys. Rev. A 84, 053627 (2011)].
