Stability of traveling pulses of cubic–quintic complex Ginzburg–Landau equation including intrapulse Raman scattering

Abstract

The complex cubic–quintic Ginzburg–Landau equation (CGLE) admits a special type of solutions called eruption solitons. Recently, the eruptions were shown to diminish or even disappear if a term of intrapulse Raman scattering (IRS) is added, in which case, self-similar traveling pulses exist. We perform a linear stability analysis of these pulses that shows that the unstable double eigenvalues of the erupting solutions split up under the effect of IRS and, following a different trajectory, they move on to the stable half-plane. The eigenfunctions characteristics explain some eruptions features. Nevertheless, for some CGLE parameters, the IRS cannot cancel the eruptions, since pulses do not propagate for the required IRS strength.