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Pattern Formation in Continuous and Coupled Systems pp 215–229Cite as

Localized Structures In Pattern-Forming Systems

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Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 115))

Abstract

A number of mechanisms that lead to the confinement of patterns to a small part of a translationally symmetric pattern-forming system are reviewed: nonadiabatic locking of fronts, global coupling and conservation laws, dispersion, and coupling to additional slow modes via gradients. Various connections with experimental results are made.

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This work was partially supported by grants from DOE (DE-FG02-92ER14303) and NASA (NAG3-2113).

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Authors and Affiliations

  1. Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL, 60208, USA

    Hermann Riecke

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  1. Hermann Riecke
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Editors and Affiliations

  1. Department of Mathematics, University of Houston, Houston, TX, 77204-4792, USA

    Martin Golubitsky

  2. Department of Chemical Engineering, University of Houston, Houston, TX, 77204-4792, USA

    Dan Luss

  3. Theoretical and Applied Mechanics, Cornell University, Ithaca, NY, 14853, USA

    Steven H. Strogatz

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Riecke, H. (1999). Localized Structures In Pattern-Forming Systems. In: Golubitsky, M., Luss, D., Strogatz, S.H. (eds) Pattern Formation in Continuous and Coupled Systems. The IMA Volumes in Mathematics and its Applications, vol 115. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1558-5_17

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  • DOI: https://doi.org/10.1007/978-1-4612-1558-5_17

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