{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T15:36:19Z","timestamp":1772292979496,"version":"3.50.1"},"reference-count":22,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2010,3]]},"abstract":"<jats:p> In this paper, bifurcation of the generalized Swift\u2013Hohenberg equation is considered. We first study the bifurcation of the generalized Swift\u2013Hohenberg equation in one spatial dimension with three kinds of boundary conditions. With the help of Liapunov\u2013Schmidt reduction, the original equation is transformed to the reduced system, and then the bifurcation analysis is carried out. Secondly, bifurcation of the generalized Swift\u2013Hohenberg equation in two spatial dimensions with periodic boundary conditions is also considered, using the perturbation method, asymptotic expressions of the nontrivial solutions bifurcated from the trivial solution are obtained. Moreover, the stability of the bifurcated solutions is discussed. <\/jats:p>","DOI":"10.1142\/s0218127410025922","type":"journal-article","created":{"date-parts":[[2010,4,9]],"date-time":"2010-04-09T07:26:31Z","timestamp":1270797991000},"page":"619-643","source":"Crossref","is-referenced-by-count":8,"title":["BIFURCATION ANALYSIS OF THE 1D AND 2D GENERALIZED SWIFT\u2013HOHENBERG EQUATION"],"prefix":"10.1142","volume":"20","author":[{"given":"HONGJUN","family":"GAO","sequence":"first","affiliation":[{"name":"Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210097, P. R. China"},{"name":"Center of Nonlinear Science, Nanjing University, Nanjing 210093, P. R. China"}]},{"given":"QINGKUN","family":"XIAO","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210097, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2012,5,2]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.74.99"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(97)00127-2"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/BF01470424"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.73.056211"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1063\/1.2746816"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2006.08.072"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8159-4"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1515\/9781400861026"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.65.851"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1137\/06067794X"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1063\/1.166142"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.51.2046"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1142\/S021812740100353X"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127402004176"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1137\/070707622"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2004.01.043"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1137\/050647232"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.3367\/UFNr.0162.199208a.0001"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.15.319"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1098\/rstb.1952.0012"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127409024542"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2007.7.441"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127410025922","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T12:48:11Z","timestamp":1565182091000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127410025922"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,3]]},"references-count":22,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2012,5,2]]},"published-print":{"date-parts":[[2010,3]]}},"alternative-id":["10.1142\/S0218127410025922"],"URL":"https:\/\/doi.org\/10.1142\/s0218127410025922","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,3]]}}}