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Grain boundaries in the Swift–Hohenberg equation

Published online by Cambridge University Press:  10 August 2012

MARIANA HARAGUS  and
ARND SCHEEL
MARIANA HARAGUS
Affiliation:
Université de Franche-Comté, Laboratoire de Mathématiques, 25030 Besançon Cedex, France email: mharagus@univ-fcomte.fr
ARND SCHEEL
Affiliation:
School of Mathematics, University of Minnesota, 206 Church St. S.E., Minneapolis, MN 55455, USA email: scheel@umn.edu
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Abstract

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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.

Keywords

Swift–Hohenberg equationRoll solutionGrain boundary
Type
Papers
Information
European Journal of Applied Mathematics , Volume 23 , Issue 6 , December 2012 , pp. 737 - 759
Copyright
Copyright © Cambridge University Press 2012

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