Abstract
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) |
|---|---|
| Pages (from-to) | 89-97 |
| Number of pages | 9 |
| Journal | International Journal of Dynamical Systems and Differential Equations |
| Volume | 1 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2007 |
Keywords
- Swift-Hohenberg equation
- interfaces
- roll solution
- zigzag instability