  {We study a model of small-amplitude traveling waves arising in a
supercritical Hopf-bifurcation, that are coupled to a slowly varying, real
field. The field is advected by the waves and, in turn, affects their stability
via a coupling to the growth rate. In the absence of dispersion we identify two
distinct shortwave instabilities. One instability induces a phase slip of the
waves and a corresponding reduction of the winding number, while the other
leads to a modulated wave structure. The bifurcation to modulated waves can be
either forward or backward, in the latter case permitting the existence of
localized, traveling pulses which are bistable with the basic, conductive
state.
