Spatiotemporal intermittency regimes of the one-dimensional complex Ginzburg-Landau equation

Abstract

Completing an earlier work, the 'phase diagram' of the one-dimensional complex Ginzburg-Landau equation is presented. In the Benjamin-Feir stable region, spatiotemporal intermittency regimes are identified which consist of patches of linearly stable plane waves separated by localized objects with a well defined dynamics. The simplest of these structures are shown to be members of a family of exact solutions discovered by Nozaki and Bekki (1985). The problem of the determination of the parameter domain of existence of spatiotemporal intermittency is discussed. In particular, given the inadequacy of the quantities usually measured to determine spatiotemporal disorder, only a rather crude determination of the limit of spatiotemporal intermittency is proposed, awaiting further knowledge on the nature, stability and interactions of the localized objects involved. In the transition region, asymptotic states with an irregular, frozen spatial structure are shown to occur. Finally, the disordered regimes observed in the Benjamin-Feir unstable region are reviewed and argued to be of the spatiotemporal intermittency type in some cases.