  We investigate Bloch oscillations of interacting cold atoms in a mean-field
framework. In general, atom-atom interaction causes dephasing and destroys
Bloch oscillations. Here, we show that Bloch oscillations are persistent if the
interaction is modulated harmonically with suitable frequency and phase. For
other modulations, Bloch oscillations are rapidly damped. We explain this
behavior in terms of collective coordinates whose Hamiltonian dynamics permits
to predict a whole family of stable solutions. In order to describe also the
unstable cases, we carry out a stability analysis for Bogoliubov excitations.
Using Floquet theory, we are able to predict the unstable modes as well as
their growth rate, found to be in excellent agreement with numerical
simulations.
