Stability of traveling pulses of cubic-quintic complex Ginzburg-Landau equation including intrapulse Raman scattering
Stability of traveling pulses of cubic-quintic complex Ginzburg-Landau equation including intrapulse Raman scattering
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Date
2011
Authors
Maria Inês Carvalho
M. Facão
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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.