Why can soliton explosions be controlled by 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.