AuthorBramburger, Jason J.
Avery, Chloe I.
AffiliationUniv Arizona, Dept Math
MetadataShow full item record
CitationBramburger, 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.
RightsCopyright © 2019, Society for Industrial and Applied Mathematics.
Collection InformationThis 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 firstname.lastname@example.org.
AbstractLocalized 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.
VersionFinal published version
SponsorsNSERCNatural Sciences and Engineering Research Council of Canada; NSFNational Science Foundation (NSF) [DMS-1408742, DMS-1714429, DMS-1439786, DMS-1148284]