  A parametrically forced Bose-Einstein condensate (BEC) is studied in the mean
field approach for the case of a general moving optical lattice. The
interaction between the atoms in the condensate and the time dependent lattice
potential leads to a novel propagating superfluid matter wave, which can be
controlled through chirp management. This system, when placed in a trap,
accelerates and undergoes rapid nonlinear compression, controlled by the chirp.
The density achieves its maximum, precisely when the matter wave changes
direction. A dynamical phase transition is identified, which takes the
superfluid phase to an insulating state. The exact expression for energy is
obtained and analyzed in detail to gain physical understanding of the chirp
management of the sinusoidal excitations and also the dynamical phase
transition.
