Long-lived matter wave Bloch oscillations and dynamical localization by time-dependent nonlinearity management

We introduce a new method to achieve long-lived Bloch oscillations and dynamical localization of matter wave gap solitons in optical lattices. The method is based on the time-dependent modulations of the nonlinearity which can be experimentally implemented by means of the Feshbach resonance technique. In particular, we show that the width of the wavepacket is preserved if the time modulations of the nonlinearity are taken proportional to the curvature of the linear band spectrum which for most typical experimental settings are well approximated by harmonic time modulations of proper frequencies.