  Mean-filed dynamics of a Bose-Einstein condensate (BEC) loaded in an optical
lattice (OL), confined by a parabolic potentials, and subjected to change of a
scattering length by means of the Feshbach resonance (FR), is considered. The
system is described by the Gross-Pitaevskii (GP) equation with varying
nonlinearity, which in a number of cases can be reduced a one-dimensional
perturbed nonlinear Schr\"{o}dinger (NLS) equation. A particular form of the
last one depends on relations among BEC parameters. We describe periodic
solutions of the NLS equation and their adiabatic dynamics due to varying
nonlinearity; carry out numerical study of the dynamics of the NLS equation
with periodic and parabolic trap potentials. We pay special attention to
processes of generation of trains of bright and dark matter solitons from
initially periodic waves.
