  We study the dynamics of the travelling interface arising from a bistable
piece-wise linear one-way coupled map lattice. We show how the dynamics of the
interfacial sites, separating the two superstable phases of the local map, is
finite dimensional and equivalent to a toral map. The velocity of the
travelling interface corresponds to the rotation vector of the toral map. As a
consequence, a rational velocity of the travelling interface is subject to
mode-locking with respect to the system parameters. We analytically compute the
Arnold's tongues where particular spatio-temporal periodic orbits exist. The
boundaries of the mode-locked regions correspond to border-collision
bifurcations of the toral map. By varying the system parameters it is possible
to increase the number of interfacial sites corresponding to a border-collision
bifurcation of the interfacial attracting cycle. We finally give some
generalizations towards smooth coupled map lattices whose interface dynamics is
typically infinite dimensional.
