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Normal form for spatial dynamics in the Swift-Hohenberg equation

• 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.
Mathematics Subject Classification: Primary: 37G05, 37L10; Secondary: 70K45.

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