  The phenomenon of dynamical localization of matter wave solitons in optical
lattices is first demonstrated and the conditions for its existence are
discussed. In addition to the trapping linear periodic potential we use a
periodic modulation of the nonlinearity in space to eliminate nonexistence
regions of gap-solitons in reciprocal space. We show that when this condition
is achieved, the observation of dynamical localization in true nonlinear regime
becomes possible. The results apply to all systems described by the periodic
nonlinear Schr\"odinger equation, including Bose-Einstein condensates of
ultracold atoms trapped in optical lattices and arrays of waveguides or
photonic crystals in nonlinear optics.
