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Applied Mathematics Colloquium
Friday, January 23, 11:30 am
Cullimore Lecture Hall II
New
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Localized patterns in the
Swift-Hohenberg equation
Björn Sandstede
Division of Applied Mathematics
Abstract
I will discuss localized stationary 1D and 2D structures such as hexagon patches,
localized radial target patterns, and localized 1D
rolls in the Swift-Hohenberg equation. All these solutions exhibit snaking: in parameter space, the localized states lie on a vertical
sine-shaped bifurcation curve so that the width of the underlying periodic pattern, such as hexagons or rolls, increases as we move up
along the bifurcation curve. I will give an overview of recent analytical and numerical work in which this phenomenon is investigated.