  We study the steady states and the coarsening dynamics in a one dimensional
driven non-conserved system modelled by the so called driven Allen-Cahn
equation, which is the standard Allen-Cahn equation with an additional driving
force. In particular, we derive equations of motion for the phase boundaries in
a phase ordering system obeying this equation using a nearest neighbour
interaction approach. Using the equations of motion we explore kink binary and
ternary interactions and analyze how the average domain size scale with respect
to time. Further, we employ numerical techniques to perform a bifurcation
analysis of the one-period stationary solutions of the equation. We then
investigate the linear stability of the two-period solutions and thereby
identify and study various coarsening modes.
