Synchronization of kinks in the two-lane totally asymmetric simple exclusion process with open boundary conditions

We study the motion of kinks in a two-lane model of the totally asymmetric simple exclusion process with open boundaries. We analytically study the motion of the kinks by a decoupling approximation. In terms of the decoupling approximation, we find that the positions of the kinks become synchronized, though the difference in the number of particles between lanes remains nonzero when the rate of lane change is asymmetric. The validity of this result is confirmed for small asymmetric cases through the Monte Carlo simulation.