Iooss, G and Rucklidge, AM (2010) On the Existence of Quasipattern Solutions of the Swift-Hohenberg Equation. Journal of Nonlinear Science, 20 (3). 361 - 394 . ISSN 0938-8974
Abstract
Quasipatterns (two-dimensional patterns that are quasiperiodic in any spatial direction) remain one of the outstanding problems of pattern formation. As with problems involving quasiperiodicity, there is a small divisor problem. In this paper, we consider 8-fold, 10-fold, 12-fold, and higher order quasipattern solutions of the Swift-Hohenberg equation. We prove that a formal solution, given by a divergent series, may be used to build a smooth quasiperiodic function which is an approximate solution of the pattern-forming partial differential equation (PDE) up to an exponentially small error.
Metadata
Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2010 Springer. Reproduced in accordance with the publisher's self-archiving policy. |
Keywords: | Bifurcations, Quasipattern, Small divisors, Gevrey series, Quasi-periodic patterns, Faraday waves, Crystals, Gravity |
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: | 12 Oct 2011 11:53 |
Last Modified: | 16 Sep 2016 14:08 |
Published Version: | http://dx.doi.org/10.1007/s00332-010-9063-0 |
Status: | Published |
Publisher: | Springer |
Refereed: | Yes |
Identification Number: | https://doi.org/10.1007/s00332-010-9063-0 |