Interfaces between rolls in the Swift-Hohenberg equation
by Mariana Haragus, Arnd Scheel
International Journal of Dynamical Systems and Differential Equations (IJDSDE), Vol. 1, No. 2, 2007

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.

Online publication date: Sun, 06-Jan-2008

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