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 by Moores [ Opt. Commun. 96 , 65 ( 1993 ) OPCOB8 0030-4018 10.1016/0030-4018(93)90524-9 ] but can be the higher-order (quintic) nonlinear refraction term. We prove that by numerically solving this equation, and we perform a 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.