  Motivated by experiments in electroconvection in nematic liquid crystals with
homeotropic alignment we study the coupled amplitude equations describing the
formation of a stationary roll pattern in the presence of a weakly-damped mode
that breaks isotropy. The equations can be generalized to describe the planarly
aligned case if the orienting effect of the boundaries is small, which can be
achieved by a destabilizing magnetic field. The slow mode represents the
in-plane director at the center of the cell. The simplest uniform states are
normal rolls which may undergo a pitchfork bifurcation to abnormal rolls with a
misaligned in-plane director.We present a new class of defect-free solutions
with spatial modulations perpendicular to the rolls. In a parameter range where
the zig-zag instability is not relevant these solutions are stable attractors,
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, for no (or very small)
damping, and away from the rotationally symmetric case, 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.
These states may provide a model for a class of poorly understood stationary
structures observed in various highly-conducting materials ("prechevrons" or
"broad domains").
