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 language||English (US)|
|Number of pages||9|
|Journal||International Journal of Dynamical Systems and Differential Equations|
|State||Published - 2007|
- Swift-Hohenberg equation
- roll solution
- zigzag instability