We numerically study the impact of self-frequency shift, self-steepening, and third-order dispersion on the erupting soliton solutions of the quintic complex Ginzburg-Landau equation. We find that the pulse explosions can be completely eliminated if these higher-order effects are properly conjugated two by two. In particular, we observe that positive third-order dispersion can compensate the self-frequency shift effect, whereas negative third-order dispersion can compensate the self-steepening effect. A stable propagation of a fixed-shape pulse is found under the simultaneous presence of the three higher-order effects.

We investigate numerically the impact of some higher-order effects, namely, self-frequency shift, self-steepening, and third-order dispersion, on the erupting soliton solutions of the quintic complex Ginzburg-Landau equation. We consider particularly the impact of these higher-order effects in the spectral domain from which we can describe the pulse characteristics in the time domain. These effects can filter in different ways the spectral perturbations that contribute to pulse explosions. We show that a proper combination of the three higher-order effects can provide a filtering of the spectral perturbations in such a way that a stable fixed-shape pulse propagation is achieved.

The eruption solitons that exist under the complex cubic-quintic Ginzburg-Landau equation (CGLE) may be eliminated by the introduction of a term that in the optical context represents intrapulse Raman scattering (IRS). The later was observed in direct numerical simulations, and here we have obtained the system of ordinary differential equations and the corresponding traveling solitons that replace the eruption solutions. In fact, we have found traveling solutions for a subset of the eruption CGLE parameter region and a wide range of the IRS parameter. However, for each set of CGLE parameters they are stable solely above a certain threshold of IRS.

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