DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:** Björn Sandstede, Brown University

**Title: ***
Localized patterns in the Swift-Hohenberg equation
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**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.

**Time:** Friday, Nov. 21, 2008, 1:30-2:30 p.m.

**Place:** Science and Tech I, Room 242

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491