Localized hole solutions and spatiotemporal chaos in the 1D complex Ginzburg-Landau equation

The cubic complex Ginzburg-Landau equation is often used to model oscillatory media. In 1D it has a one-parameter family of moving hole solutions acting as sources for traveling waves (Nozaki and Bekki). We find that this family is destroyed by arbitrarily small generic perturbations leaving only the stationary phase-slip solutions. Its stability as well as the border of spatiotemporal chaos depend crucially on the sign of the perturbation. For stabilizing perturbations one also finds oscillations of the holes. The scenario can be modeled by the Van der Pol oscillator.