Impact of the Higher-Order Reactive Nonlinearity on High-Amplitude Dissipative Solitons

In this work, the impact of the higher-order reactive nonlinearity on very high-amplitude solitons of the cubic–quintic complex Ginzburg–Landau equation is investigated. These high amplitude pulses were found in a previous work in the normal and anomalous dispersion regimes, starting from a singularity found by Akhmediev et al. We focus mainly in the normal dispersion regime, where the energy of such pulses is particularly high. In the presence of the higher-order reactive nonlinearity effect, pulse formation are observed for much higher absolute values of dispersion. Under such effect, the amplitude and the energy of the VHA pulses decrease, while their spectral range shrinks. Numerical computations are in good agreement with the predictions based on the method of moments, in the absence of the higher-order reactive nonlinearity effect. However, in the presence of this effect such agreement becomes mainly qualitative. A region of existence of the very high-amplitude pulses was found in the semi-plane defined by the normal dispersion and nonlinear gain.