SPATIOTEMPORAL INTERMITTENCY REGIMES OF THE ONE-DIMENSIONAL COMPLEX GINZBURG-LANDAU EQUATION

Completing an earlier work, the 'phase diagram' of the one-dimensional complex Ginzburg-Landau equation is presented. In the Benjamin-Feir s table region, spatiotemporal 'intermittency regimes are identified whi ch consist of patches of linearly stable plane waves separated by loca lized objects with a well defined dynamics. The simplest of these stru ctures are shown to be members of a family of exact solutions discover ed by Nozaki and Bekki. The problem of the determination of the parame ter 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 determinati on of the limit of spatiotemporal intermittency is proposed, awaiting further knowledge on the nature, stability and interactions of the loc alized objects involved. In the transition region, asymptotic states w ith 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 typ e in some cases.