Time-localized solitary wave solutions of the one-dimensional complex Ginzburg-Landau equation (CGLE) are analyzed for the case of normal group-velocity dispersion. Exact soliton solutions are found for both the cubic and the quintic CGLE. The stability of these solutions is investigated numerically. The regions in the parameter space in which stable pulselike solutions of the quintic CGLE exist are numerically determined. These regions contain subspaces where analytical solutions may be found. An investigation of the role of group-velocity dispersion changes in magnitude and sign on the spectral and temporal characteristics of the stable pulse solutions is also carried out.
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Soto‐Crespo et al. (1997) studied this question.
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