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.

Evolution of cubic–quintic complex Ginzburg–Landau erupting solitons under the effect of third-order dispersion and intrapulse Raman scattering

“…The erupting solitons have been found numerically [12] on a relatively large region of the CGLE parameter space, and were experimentally observed in passively mode-locked lasers [14]. Recently, the eruptions were shown to change or even cancel by the introduction of one or more additional terms in the CGLE [15][16][17][18][19][20]. In fact, in [18,19] we have shown that the intrapulse Raman scattering (IRS), if sufficiently strong, may move one or both unstable eigenvalues to the stable region, thus eliminating the eruptions on one side, or on both sides, of the pulse.…”

Plain and oscillatory solitons of the cubic complex Ginzburg-Landau equation with nonlinear gradient terms

“…However, it has been recently shown that the inclusion in the CGLE of a term that, in optics, models the delayed Raman scattering, allows the existence of stable solutions in a parameter region where the background is also stable [4]. Note that this higher order term has also been associated with the stabilization of erupting solitons of the quintic CGLE [5][6][7].…”

Impact of High-Order Effects on Soliton Explosions in the Complex Cubic-Quintic Ginzburg-Landau Equation

“…The interactions between third-order dispersion and other higher-order effects become important for stable pulse generation [15,16]. The influence of different HOEs on the exploding LSs in the CQGLE was studied numerically in [16][17][18][19][20][21][22][23]. In particular, it was shown that a proper combination of the three HOEs can provide a shape stabilization of an exploding LS.…”