  The center of mass dynamics of cold atoms and the Bose-Einstein condensate in
one dimensional optical lattice is considered both in the absence and in the
presence of external forcing. We discuss three situations for matter waves:
first, the cold atoms; second, sufficiently dilute condensate where the
dynamics are governed by the single particle wave packet dynamics; third,
strong interaction regime, where, inter-atomic interaction can no longer be
ignored. The analytical formalism developed for the two regimes, namely, deep
optical lattice and shallow optical lattice. Parametric dependencies of energy
spectrum and classical period, revival time and super revival are explained for
the two regimes.
  The dynamics of condensate in driven optical lattice crystal are analyzed by
studying dynamical stability of the condensate. The stability is determined by
the dispersion behavior of the condensate excited in driven optical lattice.
The recurrence behavior of the condensate close to the nonlinear resonances is
analyzed as a function of time for delicate recurrences which take place for
instance when lattice is weakly perturbed and robust recurrences which may
manifest themselves for sufficiently strong external driving force.
  The analysis is not only valid for dilute condensate but also applicable for
strongly interacting homogeneous condensate provided, the external modulation
causes no significant change in density profile of the condensate. We explain
parametric dependence of the dynamical recurrence times which can easily be
realized in laboratory experiments. In addition, we find a good agreement
between the obtained analytical results and numerical calculations. The
stability of condensate is also explored in driven optical lattice numerically.
