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Applied Mathematics Colloquium


Friday, January 23, 11:30 am
Cullimore Lecture Hall II
New Jersey Institute of Technology

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Localized patterns in the Swift-Hohenberg equation

 

Björn Sandstede

Division of Applied Mathematics

Brown University

Providence, RI

 

 

 

 

 

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.