Zigzag structures and domain walls in electroconvection of nematic liquid crystal

To describe the secondary-bifurcation scenario in ac-driven electroconvection of a planarly aligned nematic liquid crystal layer, we have constructed a generic phase equation coupled to the cinsertion mark director. The equations are applicable in particular in the vicinity of the codimension-2 point, where the zigzag and the abnormal roll instabilities meet. This point is also the origin of a line of homoclinic bifurcations, which separates a region where one has stationary zigzag walls from one with spontaneously accelerated abnormal roll walls. The final velocity of the walls depends linearly on the distance from the bifurcation. We analyze the scenario analytically, test it numerically and propose an experimental check.