{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T12:30:59Z","timestamp":1787229059118,"version":"build-2736575974"},"reference-count":29,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Dyn. Syst."],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>Recent work on the behavior of localized states in pattern-forming partial differential equations has focused on the traditional model Swift\u2013Hohenberg 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\u2013Hohenberg 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\u2013Hohenberg equation with the analogous solutions to the usual Swift\u2013Hohenberg equation.<\/jats:p>","DOI":"10.1137\/110843976","type":"journal-article","created":{"date-parts":[[2012,3,2]],"date-time":"2012-03-02T08:33:56Z","timestamp":1330677236000},"page":"261-284","source":"Crossref","is-referenced-by-count":46,"title":["Localized States in an Extended Swift\u2013Hohenberg Equation"],"prefix":"10.1137","volume":"11","author":[{"given":"John","family":"Burke","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jonathan H. 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