A. Scheel and Q. Wu
The authors study grain boundaries in the Swift-Hohenberg equation. Grain boundaries arise as stationary interfaces between roll solutions of different orientations. Their analysis shows that such stationary interfaces exist near onset of instability for arbitrary angles between the roll solutions. This extends prior work in [Haragus and Scheel, see below] where the analysis was restricted to large angles, that is, weak bending near the grain boundary. The main new difficulty stems from possible interactions of the primary modes with other resonant modes. They generalize the normal form analysis in [M. Haragus and A. Scheel, Europ. J. Appl. Math. 23, 737–759 (2012)] and develop a singular perturbation approach to treat resonances.