  We demonstrate that nonlinearity plays a constructive role in supporting the
robustness of dynamical localization in a model which is discrete, in one
dimension and continuous in the orthogonal one. In the linear regime,
time-periodic modulation of the gradient strength along the discrete axis leads
to the usual rapid spread of an initially confined wave packet. Addition of the
cubic nonlinearity makes the dynamics drastically different, inducing robust
localization of moving wave packets. Similar nonlinearity-induced effects are
also produced by combinations of static and oscillating linear potentials. The
predicted nonlinearity-induced dynamical localization can be realized in
photonic lattices and Bose-Einstein condensates.
