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Interfaces between rolls in the Swift-Hohenberg equation

Published Online:pp 89-97https://doi.org/10.1504/IJDSDE.2007.016510

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