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Uniformly translating solutions of the one-dimensional complex Ginzburg-Landau equation are studied near a subcritical bifurcation. Two classes of solutions are singled out since they are often produced starting from localized initial conditions: moving fronts and stationary pulses. A particular exact analytic front solution is found, which is conjectured to control the relative stability of pulses and fronts. Numerical solutions of the Ginzburg-Landau equation confirm the predictions based on this conjecture.
Saarloos et al. (Mon,) studied this question.