Title: Interfaces between rolls in the Swift-Hohenberg equation

Authors: Mariana Haragus, Arnd Scheel

Addresses: Laboratoire de Mathematiques, Universite de Franche-Comte, 16 route de Gray, 25030 Besancon cedex, France. ' School of Mathematics, University of Minnesota, 206 Church St. S.E., Minneapolis, MN 55455, USA

Abstract: We study the existence of interfaces between stripe or roll solutions in the Swift-Hohenberg 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.

Keywords: interfaces; roll solutions; stripe solutions; spatial dynamics; Swift-Hohenberg equation; zigzag instability; centre manifold reduction; ODEs; ordinary differential equations.

DOI: 10.1504/IJDSDE.2007.016510

International Journal of Dynamical Systems and Differential Equations, 2007 Vol.1 No.2, pp.89 - 97

Published online: 06 Jan 2008 *

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