  The Josephson dynamics of the Bose-Einstein condensation with Raman-induced
spin-orbit coupling is investigated. A quasi-1D trap is divided into two
reservoirs by an optical barrier. Before the tunneling between the reservoirs
is turned on, the system stays in its equilibrium ground state. For different
spin-orbit coupling parameters and interaction strengthes, the ground state
displays a rich phase diagram. In this work we focus on the plane wave phase
and the stripe phase. Our calculation shows that, when the tunneling is turned
on, the plane wave phase evolves into a dynamical stripe phase, that is, the
density of the particle changes from uniform to periodically modulated.
Basically, this stripe is described by a sine function and the wave length, the
amplitude and the initial phase of the function are all varying with time. If
the system stays in stripe phase initially, the stripes become ``sliding" when
the tunneling is turned on, which reflects the running of one of the phases of
the wave function.
