{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:26:35Z","timestamp":1787232395042,"version":"build-2736575974"},"reference-count":24,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Dyn. Syst."],"published-print":{"date-parts":[[2005,1]]},"abstract":"<jats:p>In this article we construct, both asymptotically and numerically, multibump, blow-up, self-similar solutions to the complex Ginzburg--Landau equation (CGL) in the limit of small dissipation. Through a careful asymptotic analysis, involving a balance of both algebraic and exponential terms, we determine the parameter range over which these solutions may exist. Most intriguingly, we determine a branch of solutions that are not perturbations of solutions to the nonlinear Schr\u00f6dinger equation (NLS); moreover, they are not monotone, but they are stable. Furthermore, these axisymmetric ring-like solutions exist over a broader parameter regime than the monotone profile.<\/jats:p>","DOI":"10.1137\/040610866","type":"journal-article","created":{"date-parts":[[2005,9,7]],"date-time":"2005-09-07T21:00:16Z","timestamp":1126126816000},"page":"649-678","source":"Crossref","is-referenced-by-count":14,"title":["Multibump, Blow-Up, Self-Similar Solutions of the Complex Ginzburg--Landau Equation"],"prefix":"10.1137","volume":"4","author":[{"given":"C. J.","family":"Budd","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"V.","family":"Rottsch\u00e4fer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J. F.","family":"Williams","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,8,7]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.74.99"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107050242"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(86)90140-5"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139900382395"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1999.6262"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827594272025"},{"key":"R7","unstructured":"C. J. Budd and J. F. Williams,\n                      Optimal Grids and Uniform Error Estimates for PDEs with Blow\u2010Up\n                      , in preparation, 2004."},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112074001765"},{"key":"R9","doi-asserted-by":"crossref","unstructured":"R. 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Rabinowitz, ed., Gordon and Breach, New York, 1988, pp. 87\u2013114."},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.2001.7814"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/16\/3\/308"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112071001733"},{"key":"R24","volume-title":"The nonlinear Schr\u00f6dinger equation","author":"Sulem Catherine","year":"1999"}],"container-title":["SIAM Journal on Applied Dynamical Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/040610866","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T12:46:27Z","timestamp":1787229987000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/040610866"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,1]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2005,1]]}},"alternative-id":["10.1137\/040610866"],"URL":"https:\/\/doi.org\/10.1137\/040610866","relation":{},"ISSN":["1536-0040"],"issn-type":[{"value":"1536-0040","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,1]]}}}