Interfaces between rolls in the Swift-Hohenberg equation

Mariana Haragus, Arnd Scheel

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We study the existence of interfaces between stripe or roll solutions in the SwiftHohenberg equation. We prove the existence of two different types of interfaces: corner-like interfaces, also referred to as knee solutions, and step-like interfaces. The analysis relies upon a spatial dynamics formulation of the existence problem and an equivariant centre-manifold reduction. In this setting, the interfaces are found as heteroclinic and homoclinic orbits of a reduced system of ODEs.

Original languageEnglish (US)
Pages (from-to)89-97
Number of pages9
JournalInternational Journal of Dynamical Systems and Differential Equations
Volume1
Issue number2
DOIs
StatePublished - 2007

Keywords

  • Swift-Hohenberg equation
  • interfaces
  • roll solution
  • zigzag instability

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