Dislocations in an Anisotropic Swift-Hohenberg Equation

Mariana Haragus, Arnd Scheel

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

We study the existence of dislocations in an anisotropic Swift-Hohenberg equation. We find dislocations as traveling or standing waves connecting roll patterns with different wavenumbers in an infinite strip. The proof is based on a bifurcation analysis. Spatial dynamics and center-manifold reduction yield a reduced, coupled-mode system of differential equations. Existence of traveling dislocations is then established by showing that this reduced system possesses robust heteroclinic orbits.

Original languageEnglish (US)
Pages (from-to)311-335
Number of pages25
JournalCommunications in Mathematical Physics
Volume315
Issue number2
DOIs
StatePublished - Oct 2012

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