  We consider spin-orbit coupled Bose Einstein Condensate in presence of linear
and nonlinear optical lattices within the framework of quasi-one-dimensional
Gross-Pitaevskii equation. The population imbalance between the states changes
periodically with time and the oscillation amplitude depends sensitively on the
initial phase. The optical lattice is found to change phase velocity of the
oscillation of population imbalance. This oscillation can also be arrested
beyond critical values of parameters. We find that the optical lattice can
efficiently be used to control the critical point.
