  The cubic Complex Ginzburg-Landau Equation (CGLE) has a one parameter family
of traveling localized source solutions. These so called 'Nozaki-Bekki holes'
are (dynamically) stable in some parameter range, but always structually
unstable: A perturbation of the equation in general leads to a (positive or
negative) monotonic acceleration or an oscillation of the holes. This confirms
that the cubic CGLE has an inner symmetry. As a consequence small perturbations
change some of the qualitative dynamics of the cubic CGLE and enhance or
suppress spatio-temporal intermittency in some parameter range. An analytic
stability analysis of holes in the cubic CGLE and a semianalytical treatment of
the acceleration instability in the perturbed equation is performed by using
matching and perturbation methods. Furthermore we treat the asymptotic
hole-shock interaction. The results, which can be obtained fully analytically
in the nonlinear Schroedinger limit, are also used for the quantitative
description of modulated solutions made up of periodic arrangements of
traveling holes and shocks.

Pattern Formation and Solitons;Pattern Formation and Solitons