Small-amplitude grain boundaries of arbitrary angle in the Swift-Hohenberg equation

A. Scheel, Q. Wu

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)203-232
Number of pages30
JournalZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Volume94
Issue number3
DOIs
StatePublished - Mar 2014

Keywords

  • Grain boundary
  • Normal forms
  • Singular perturbation
  • Spatial dynamics
  • Swift-Hohenberg equation

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