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We study the motion of a grain boundary separating two otherwise stationarydomains of hexagonal symmetry. Starting from an order parameter equationappropriate for hexagonal patterns, a multiple scale analysis leads to ananalytical equation of motion for the boundary that shares many properties withthat of a crystalline solid. We find that defect motion is generically opposedby a pinning force that arises from non-adiabatic corrections to the standardamplitude equation. The magnitude of this force depends sharply on themis-orientation angle between adjacent domains so that the most easily pinnedgrain boundaries are those with an angle between four and eight degrees.Although pinning effects may be small, they do not vanish asymptotically nearthe onset of this subcritical bifurcation, and can be orders of magnitudelarger than those present in smectic phases that bifurcate supercritically

Weakly Nonlinear Theory of Grain Boundary Motion in Patterns with Crystalline Symmetry