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Small‐amplitude grain boundaries of arbitrary angle in the Swift‐Hohenberg equation
Author(s) -
Scheel A.,
Wu Q.
Publication year - 2014
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201200172
Subject(s) - grain boundary , swift , singular perturbation , perturbation (astronomy) , amplitude , instability , mathematical analysis , physics , work (physics) , mathematics , geometry , mechanics , materials science , microstructure , optics , thermodynamics , quantum mechanics , astrophysics , metallurgy
We study grain boundaries in the Swift‐Hohenberg equation. Grain boundaries arise as stationary interfaces between roll solutions of different orientations. Our analysis shows that such stationary interfaces exist near onset of instability for arbitrary angles between the roll solutions. This extends prior work in [6] 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. We generalize the normal form analysis in [6] and develop a singular perturbation approach to treat resonances.