  In pattern-forming systems, competition between patterns with different wave
numbers can lead to domain structures, which consist of regions with differing
wave numbers separated by domain walls. For domain structures well above
threshold we employ the appropriate phase equation and obtain detailed
qualitative agreement with recent experiments. Close to threshold a
fourth-order Ginzburg-Landau equation is used which describes a steady
bifurcation in systems with two competing critical wave numbers. The existence
and stability regime of domain structures is found to be very intricate due to
interactions with other modes.
  In contrast to the phase equation the Ginzburg-Landau equation allows a
spatially oscillatory interaction of the domain walls. Thus, close to threshold
domain structures need not undergo the coarsening dynamics found in the phase
equation far above threshold, and can be stable even without phase
conservation. We study their regime of stability as a function of their
(quantized) length. Domain structures are related to zig-zags in
two-dimensional systems. The latter are therefore expected to be stable only
when quenched far enough beyond the zig-zag instability.
