Abstract
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 short-wave 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.
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