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• W2124399215 abstract "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." @default.
• W2124399215 created "2016-06-24" @default.
• W2124399215 creator A5033496719 @default.
• W2124399215 creator A5064073614 @default.
• W2124399215 date "2012-01-01" @default.
• W2124399215 modified "2023-09-25" @default.
• W2124399215 title "Localized States in an Extended Swift–Hohenberg Equation" @default.
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• W2124399215 doi "https://doi.org/10.1137/110843976" @default.
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