PULSE SOLUTIONS OF THE CUBIC-QUINTIC COMPLEX GINZBURG-LANDAU EQUATIONIN THE CASE OF NORMAL DISPERSION

Time-localized solitary wave solutions of the one-dimensional complex Ginzburg-Landau equation (CGLE) are analyzed for the case of normal gr oup-velocity dispersion. Exact soliton solutions are found for both th e cubic and the quintic CGLE. The stability of these solutions is inve stigated numerically. The regions in the parameter space in which stab le pulselike solutions of the quintic CGLE exist are numerically deter mined. These regions contain subspaces where analytical solutions may be found. An investigation of the role of group-velocity dispersion ch anges in magnitude and sign on the spectral and temporal characteristi cs of the stable pulse solutions is also carried out.