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patt-sol1996★ 26 cited
Geometric Stability Analysis for Periodic Solutions of the Swift-Hohenberg Equation
J. -P. Eckmann, C. E. Wayne, P. Wittwer
In this paper we describe invariant geometrical ~structures in the phase space of the Swift-Hohenberg equation in a neighborhood of its periodic stationary states. We show that in…
patt-sol1994★ 26 cited
On the validity of mean-field amplitude equations for counterpropagating wavetrains
R. D. Pierce, C. E. Wayne
We rigorously establish the validity of the equations describing the evolution of one-dimensional long wavelength modulations of counterpropagating wavetrains for a hyperbolic mode…