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) |
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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