PROPAGATING CONFINED STATES IN PHASE DYNAMICS

We show that the nonlinear phase equation that applies to propagating patterns allows for a large range of parameter values for propagating confined states for which a spatially localized region with wavelengths different from that of the background travels on this background. This phenomenon is the generalization of the stationary confined states predicted a few years ago by the authors, which have since been seen experimentally in various systems. We suggest that the propagating confined states found here could arise in spirals in Taylor vortex flow or in convective systems showing traveling waves far above onset. We find that the propagating confined states can be replaced by a pattern that is irregular in space and time as the control parameter in the nonlinear phase equation is varied.