Abstract
We study the existence of grain boundaries in the Swift-Hohenberg equation. The analysis relies on a spatial dynamics formulation of the existence problem and a centre-manifold reduction. In this setting, the grain boundaries are found as heteroclinic orbits of a reduced system of ordinary differential equations in normal form. We show persistence of the leading-order approximation using transversality induced by wavenumber selection.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 737-759 |
| Number of pages | 23 |
| Journal | European Journal of Applied Mathematics |
| Volume | 23 |
| Issue number | 6 |
| DOIs | |
| State | Published - Dec 2012 |
Keywords
- Grain boundary
- Roll solution
- Swift-Hohenberg equation