  We study the phase distribution and its dynamics in spin-orbit coupled two
component ultracold Bosons for finite size system. Using an inhomogeneous
meanfield analysis we demonstrate how phase distribution evolves as we tune the
spin-orbit coupling $\gamma$ and $t$, the spin-independent hopping. For
$t>>\gamma$ we find the homogeneous superfluid phase. As we increase $\gamma$,
differences in the phases of the order parameter grows leading to twisted
superfluid phase. For $t \sim \gamma$ competing orderings in the phase
distribution is observed. At large $\gamma$ limit a Ferro-Magnetic stripe
ordering appears along the diagonal. We explain that this is due to the
frustration bought in by the spin-orbit interaction. Isolated vortex formation
is also shown to appear. We also investigate the possible collective modes. In
deep superfluid regime we derive the equation of motion for the phases
following a semi-classical approximation. Imaginary frequencies indicating the
damped modes are seen to appear and the dynamics of lowest normal modes are
discussed.
