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swift–hohenberg equation

European Journal of Applied Mathematics (1)

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Grain boundaries in the Swift–Hohenberg equation
MARIANA HARAGUS, ARND SCHEEL
Journal:

European Journal of Applied Mathematics / Volume 23 / Issue 6 / December 2012

Published online by Cambridge University Press:

10 August 2012, pp. 737-759
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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.