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Geometric Stability Analysis for Periodic Solutions of the Swift-Hohenberg Equation

Published inCommunications in Mathematical Physics, vol. 190, no. 1, p. 173-211
Publication date1997
Abstract

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 spite of the fact that these states are only marginally stable (i.e., the linearized problem about these states has continuous spectrum extending all the way up to zero), there exist finite dimensional invariant manifolds in the phase space of this equation which determine the long-time behavior of solutions near these stationary solutions. In particular, using this point of view, we obtain a new demonstration of Schneider's recent proof that these states are nonlinearly stable.

Keywords
  • Manifold
  • Phase space
  • Stationary state
  • Stability analysis
  • Periodic solution
Citation (ISO format)
ECKMANN, Jean-Pierre, WAYNE, C. Eugene, WITTWER, Peter. Geometric Stability Analysis for Periodic Solutions of the Swift-Hohenberg Equation. In: Communications in Mathematical Physics, 1997, vol. 190, n° 1, p. 173–211. doi: 10.1007/s002200050238
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Article (Published version)
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Identifiers
ISSN of the journal1432-0916
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