Abstract
We report on the experimental study of a novel time-dependent localized state in the electroconvection of a nematic liquid crystal inside a container of very large aspect ratio. At threshold the convective rolls propagate inside isolated domains well localized in space. The phase propagation is attributed to a slow lateral drift of the ionic charges, while the localization, which is not due to finite-size effects, could result from the nonlinear focusing of a broad band of dispersive modes.