Grain boundaries in the Swift-Hohenberg equation

Mariana Haragus, Arnd Scheel

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We study the existence of grain boundaries in the Swift-Hohenberg equation. The analysis relies on a spatial dynamics formulation of the existence problem and a centre-manifold reduction. In this setting, the grain boundaries are found as heteroclinic orbits of a reduced system of ordinary differential equations in normal form. We show persistence of the leading-order approximation using transversality induced by wavenumber selection.

Original languageEnglish (US)
Pages (from-to)737-759
Number of pages23
JournalEuropean Journal of Applied Mathematics
Volume23
Issue number6
DOIs
StatePublished - Dec 2012

Keywords

  • Grain boundary
  • Roll solution
  • Swift-Hohenberg equation

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