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Normal form for spatial dynamics in the Swift-Hohenberg equation

Pages: 170 - 180, Issue Special, September 2007

 Abstract        Full Text (203.1K)              

John Burke - University of California, Department of Physics, Berkeley, CA 94720, United States (email)
Edgar Knobloch - Department of Physics, University of California, Berkeley, CA 94720, United States (email)

Abstract: 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: 70K45.

Received: August 2006;      Revised: January 2007;      Published: September 2007.