Gandhi, P, Beaume, C and Knobloch, E (2015) A New Resonance Mechanism in the Swift--Hohenberg Equation with Time-Periodic Forcing. SIAM Journal on Applied Dynamical Systems, 14 (2). pp. 860-892. ISSN 1536-0040
Abstract
The generalized Swift--Hohenberg equation with a quadratic-cubic nonlinearity is used to study the persistence and decay of localized patterns in the presence of time-periodic parametric forcing. A novel resonance phenomenon between the forcing period and the time required to nucleate one wavelength of the pattern outside the pinning region is identified. The resonance generates distinct regions in parameter space characterized by the net number of wavelengths gained or lost in one forcing cycle. These regions are well described by an asymptotic theory based on the wavelength nucleation/annihilation time near the boundaries of the pinning region. The resulting theory leads to predictions that are qualitatively correct and, in some cases, provide quantitative agreement with numerical simulations.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Keywords: | Swift--Hohenberg equation, localized structures, parametric forcing |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 14 Feb 2017 14:08 |
Last Modified: | 14 Feb 2017 14:08 |
Published Version: | https://doi.org/10.1137/14099468X |
Status: | Published |
Publisher: | Society for Industrial and Applied Mathematics |
Identification Number: | 10.1137/14099468X |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:109054 |