Worm structure in the modified Swift-Hohenberg equation for electroconvection

An anisotropic complex Swift-Hohenberg equation is proposed to study pattern formation in electroconvection. In the subcritical regime, a localized state is found in two dimensions, which resembles the “worm” state observed in recent experiment by M. Dennin et al. [Phys. Rev. Lett. 77, 2475 (1996); Science 272, 388 (1996)]. In the corresponding one-dimensional model, a stationary pulse state is discovered, due to a nonadiabatic effect, and it is shown to explain the localization of the “worm” state in the two-dimensional model. Based on these results, we believe that the initial bifurcation should be subcritical where the “worm” state is observed, and further experiment is suggested to test this scenario.