Nematic liquid crystals is probably the simplest type of intrinsically anisotropic fluid and provide model systems for a wide variety of interesting nonlinear dynamical phenomena like electrically or thermally driven convection instabilities. In nematics the mean orientation of the rodlike molecules is described by the director. Electroconvection (EC) driven by an ac voltage is commonly observed in thin nematic layers sandwiched between glass plates with transparent electrodes.
We have studied the coupled amplitude equations describing the formation of a stationary roll pattern in the presence of a weakly damped mode that breaks isotropy. The simplest uniform states are normal rolls, which may undergo a pitchfork bifurcation to abnormal rolls with a misaligned in-plane director. We present defect-free solutions with spatial modulations perpendicular to the rolls. These solutions are stable attractors (in a certain regime), as observed in experiments. We also present two-dimensionally modulated states with and without defects which result from the destabilization of the one-dimensionally modulated structures. Finally, we find static chevrons made up of a periodic arrangement of defect chains or bands of defects separating homogeneous regions of oblique rolls with very small amplitude. [PRE, 2003]