Role of the quintic nonlinear refractive term in the stability of dissipative solitons of the complex Ginzburg-Landau equation

We revisit the role of the quintic terms of the complex cubic-quintic Ginzburg-Landau equation in the generation of stable dissipative solitons. Using direct numerical simulations and a qualitative analysis, we show that the presence of one of the two quintic terms is a sine qua non. However, this term is not necessarily the quintic gain saturation term as had been demonstrated byMoores [Opt. Commun. 96, 65 (1993)] but can be the higher-order (quintic) nonlinear refraction term.We prove that by numerically solving this equation, and we performa qualitative analysis that shows that the negative soliton chirp, anomalous dispersion, and spectral filtering are the physical effects responsible for gain saturation in this case.