  Motivated by previous results showing that the addition of a linear
dispersive term to the two-dimensional Kuramoto-Sivashinsky equation has a
dramatic effect on the pattern formation, we study the Swift-Hohenberg equation
with an added linear dispersive term, the dispersive Swift-Hohenberg equation
(DSHE). The DSHE produces stripe patterns with spatially extended dislocations
that we call seam defects. In contrast to the dispersive Kuramoto-Sivashinsky
equation, the DSHE has a narrow band of unstable wavelengths close to an
instability threshold. This allows for analytical progress to be made. We show
that the amplitude equation for the DSHE close to threshold is a special case
of the anisotropic complex Ginzburg-Landau equation (ACGLE) and that seams in
the DSHE correspond to spiral waves in the ACGLE. Seam defects and the
corresponding spiral waves tend to organize themselves into chains, and we
obtain formulas for the velocity of the spiral wave cores and for the spacing
between them. In the limit of strong dispersion, a perturbative analysis yields
a relationship between the amplitude and wavelength of a stripe pattern and its
propagation velocity. Numerical integrations of the ACGLE and the DSHE confirm
these analytical results.
