The spatio-temporal evolution of the vortex sheet separating two finit
e-depth layers of immiscible fluids is examined in the vicinity of thr
eshold when spatially periodic forcing is imposed at the horizontal bo
undaries. As a result of the Galilean invariance of the problem, the i
nterface deformation is shown to satisfy a coupled system of evolution
equations involving not only the usual ''short-wave'' at the critical
wavenumber but also a shallow-water ''long-wave'' associated with the
mean elevation of the interface. The weakly nonlinear model is furthe
r studied in the Boussinesq approximation where it reduces to a forced
Klein-Gordon equation. Thus, the secondary Benjamin-Feir instability
of nonlinear Stokes wavetrains is analysed in the absence of forcing.
When spatial forcing is reintroduced, the competition between the impo
sed external length scale and the natural length scale of the interfac
e is shown analytically to give rise to one-dimensional propagating Si
ne-Gordon phase solitons. Numerical simulations of the Klein-Gordon ev
olution model fully confirm this prediction and also lead to the deter
mination of the range of stability of phase solitons.