American Institute of Mathematical Sciences

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2007, 2007(Special): 170-180. doi: 10.3934/proc.2007.2007.170

Normal form for spatial dynamics in the Swift-Hohenberg equation

John Burke 1, and  Edgar Knobloch 2,

1. 

University of California, Department of Physics, Berkeley, CA 94720, United States
2. 

Department of Physics, University of California, Berkeley, CA 94720, United States

Received  August 2006 Revised  January 2007 Published  September 2007

The reversible Hopf bifurcation with 1:1 resonance holds the key to the presence of spatially localized steady states in many partial differential equations on the real line. Two different techniques for computing the normal form for this bifurcation are described and applied to the Swift-Hohenberg equation with cubic/quintic and quadratic/cubic nonlinearities.
Keywords: Normal form, Swift-Hohenberg equation, localized states..
Mathematics Subject Classification: Primary: 37G05, 37L10; Secondary: 70K4.
Citation: John Burke, Edgar Knobloch. Normal form for spatial dynamics in the Swift-Hohenberg equation. Conference Publications, 2007, 2007 (Special) : 170-180. doi: 10.3934/proc.2007.2007.170
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