Localized states in an extended Swift–Hohenberg equation


Burke, J. and Dawes, J. H. P., 2012. Localized states in an extended Swift–Hohenberg equation. SIAM Journal on Applied Dynamical Systems, 11 (1), pp. 261-284.

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    Recent work on the behavior of localized states in pattern-forming partial differential equations has focused on the traditional model Swift-Hohenberg equation which, as a result of its simplicity, has additional structure; it is variational in time and conservative in space. In this paper we investigate an extended Swift-Hohenberg equation in which nonvariational and nonconservative effects play a key role. Our work concentrates on aspects of this much more complicated problem. First we carry out the normal form analysis of the initial pattern-forming instability that leads to small-amplitude localized states. Next we examine the bifurcation structure of the large-amplitude localized states. Finally, we investigate the temporal stability of one-peak localized states. Throughout, we compare the localized states in the extended Swift-Hohenberg equation with the analogous solutions to the usual Swift-Hohenberg equation.


    Item Type Articles
    CreatorsBurke, J.and Dawes, J. H. P.
    Related URLs
    URLURL Type
    DepartmentsFaculty of Science > Mathematical Sciences
    Research CentresCentre for Mathematical Biology
    Publisher StatementBurkeDawesSIADS2012.pdf: © 2012 Society for Industrial and Applied Mathematics
    ID Code30647


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