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    Localized Radial Roll Patterns in Higher Space Dimensions

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    18m1218728.pdf
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    Author
    Bramburger, Jason J.
    Altschuler, Dylan
    Avery, Chloe I.
    Sangsawang, Tharathep
    Beck, Margaret
    Carter, Paul
    Sandstede, Björn
    Affiliation
    Univ Arizona, Dept Math
    Issue Date
    2019-08-01
    Keywords
    Swift-Hohenberg equation
    singular perturbation
    localized pattern
    snaking bifurcation
    
    Metadata
    Show full item record
    Publisher
    SIAM PUBLICATIONS
    Citation
    Bramburger, J. J., Altschuler, D., Avery, C. I., Sangsawang, T., Beck, M., Carter, P., & Sandstede, B. (2019). Localized radial roll patterns in higher space dimensions. SIAM Journal on Applied Dynamical Systems, 18(3), 1420-1453.
    Journal
    SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
    Rights
    Copyright © 2019, Society for Industrial and Applied Mathematics.
    Collection Information
    This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.
    Abstract
    Localized roll patterns are structures that exhibit a spatially periodic profile in their center. When following such patterns in a system parameter in one space dimension, the length of the spatial interval over which these patterns resemble a periodic profile stays either bounded, in which case branches form closed bounded curves ("isolas"), or the length increases to infinity so that branches are unbounded in function space ("snaking"). In two space dimensions, numerical computations show that branches of localized rolls exhibit a more complicated structure in which both isolas and snaking occur. In this paper, we analyze the structure of branches of localized radial roll solutions in dimension 1+epsilon, with 0 < epsilon << 1, through a perturbation analysis. Our analysis sheds light on some of the features visible in the planar case.
    ISSN
    1536-0040
    DOI
    10.1137/18m1218728
    Version
    Final published version
    Sponsors
    NSERCNatural Sciences and Engineering Research Council of Canada; NSFNational Science Foundation (NSF) [DMS-1408742, DMS-1714429, DMS-1439786, DMS-1148284]
    ae974a485f413a2113503eed53cd6c53
    10.1137/18m1218728
    Scopus Count
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    UA Faculty Publications

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