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The key ingredient to obtain the global well-posedness is that we achieve a priori estimates of the solution in modulation spaces by utilizing the power series expansion of the perturbation determinant introduced by Killip\u2013Vi\u015fan\u2013Zhang for completely integrable PDEs.<\/jats:p>","DOI":"10.1137\/24m1679914","type":"journal-article","created":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T07:06:53Z","timestamp":1782889613000},"page":"3267-3305","source":"Crossref","is-referenced-by-count":0,"title":["Global Well-Posedness for the Fourth-Order Nonlinear Schr\u00f6dinger Equation"],"prefix":"10.1137","volume":"58","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-7960-8401","authenticated-orcid":true,"given":"Mingjuan","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Mathematics, Jinan University, Guangzhou 510632, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8826-9615","authenticated-orcid":true,"given":"Yufeng","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Science, Jimei University, Xiamen 361021, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yaqing","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Jinan University, Guangzhou 510632, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,7,1]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s00028-024-01016-y"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2007.06.024"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.4310\/CMS.2020.v18.n4.a2"},{"key":"ref4","first-page":"2315","volume":"13","author":"Chen M. 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