HOLE SOLUTIONS IN THE 1D COMPLEX GINZBURG-LANDAU EQUATION

The cubic Complex Ginzburg-Landau Equation (CGLE) has a one parameter family of traveling localized source solutions. These so called ''Noza ki-Bekki holes'' are (dynamically) stable in some parameter range, but always structurally unstable: A perturbation of the equation in gener al leads to a (positive or negative) monstonic acceleration or an osci llation of the holes. This confirms that the cubic CGLE has an inner s ymmetry. As a consequence small perturbations change some of the quali tative dynamics of the cubic CGLE and enhance or suppress spatio-tempo ral intermittency in some parameter range. An analytic stability analy sis of holes in the cubic CGLE and a semianalytical treatment of the a cceleration instability in the perturbed equation is performed by usin g matching and perturbation methods. Furthermore we treat the asymptot ic hole-shock interaction. The results, which can be obtained fully an alytically in the nonlinear Schrodinger limit, are also used for the q uantitative description of modulated solutions made up of periodic arr angements of traveling holes and shocks.