  We study a system composed of two parallel totally asymmetric simple
exclusion processes with open boundaries, where the particles move in the two
lanes in opposite directions and are allowed to jump to the other lane with
rates inversely proportional to the length of the system. Stationary density
profiles are determined and the phase diagram of the model is constructed in
the hydrodynamic limit, by solving the differential equations describing the
steady state of the system, analytically for vanishing total current and
numerically for nonzero total current. The system possesses phases with a
localized shock in the density profile in one of the lanes, similarly to
exclusion processes endowed with nonconserving kinetics in the bulk. Besides,
the system undergoes a discontinuous phase transition, where coherently moving
delocalized shocks emerge in both lanes and the fluctuation of the global
density is described by an unbiased random walk. This phenomenon is analogous
to the phase coexistence observed at the coexistence line of the totally
asymmetric simple exclusion process, however, as a consequence of the
interaction between lanes, the density profiles are deformed and in the case of
asymmetric lane change, the motion of the shocks is confined to a limited
domain.
