Control of complex Ginzburg-Landau equation eruptions using intrapulse Raman scattering and corresponding traveling solutions

The eruption solitons that exist under the complex cubic-quintic Ginzburg-Landau equation (CGLE) may be eliminated by the introduction of a term that in the optical context represents intrapulse Raman scattering (IRS). The later was observed in direct numerical simulations, and here we have obtained the system of ordinary differential equations and the corresponding traveling solitons that replace the eruption solutions. In fact, we have found traveling solutions for a subset of the eruption CGLE parameter region and a wide range of the IRS parameter. However, for each set of CGLE parameters they are stable solely above a certain threshold of IRS.