Holes and chaotic pulses of traveling waves coupled to a long-wave mode

Localized traveling-wave pulses and holes, i.e. localized regions of vanishing wave amplitude, are investigated in a real Ginzburg-Landau equation coupled to a long-wave mode. In certain parameter regimes the pulses exhibit a Hopf bifurcation which leads to a breathing motion. Subsequently the oscillations undergo period-doubling bifurcations and become chaotic.