Figure 1

(a) Region of existence of stable fixed points for the dynamical system given by Eq. (7) (dark shade) in the $(D,ϵ)$ plane. The soliton energy $Q$ and the width $w$ increase to infinitely large values near the resonance curve shown in the middle by a solid line. (b) Numerical simulations of the CGLE from Ref. 3. The approximation based on Eq. (7) is in reasonably good qualitative agreement with numerical simulations, apart from the fact that the stable soliton solutions are only found on the right-hand side of the resonance curve in the simulations. Consequently, the resonance curve (black) is the left-hand side border of the gray region containing stable solitons. The light gray region on the right-hand side of plot (a) corresponds to periodic solutions. These are pulsating solitons, also found in numerical simulations [3] but not shown here in (b).Reuse & Permissions

Figure 2

(a) Reduced model pulse profiles and (b) soliton spectra for the set of parameters shown inside the plots. The qualitative changes in both the profiles and the spectra as $D$ is varied agree well with those of the exact soliton solutions in Ref. 3.Reuse & Permissions

Figure 3

(a) Reduced model pulse profiles and (b) soliton spectra for the set of parameters shown inside the figures. The qualitative changes, in both the profiles and the spectra, as $ϵ$ is varied agree well with those of the exact soliton solutions in Ref. 3.Reuse & Permissions

Figure 4

(a) Soliton energy $Q$ vs dispersion parameter $D$ for three $ϵ$ values in the generalized Gaussian model with $4m=1$. In the exact simulations, the fixed soliton curves on the left-hand side of the asymptotes do not appear. They would not be observed in experiments and may represent unstable solitons. (b) Chirp parameter $c$ vs $D$ for the same simulations. Vertical lines show that the chirp parameter is zero at resonance.Reuse & Permissions