{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T08:36:03Z","timestamp":1648542963372},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2007,7,12]],"date-time":"2007-07-12T00:00:00Z","timestamp":1184198400000},"content-version":"unspecified","delay-in-days":1136,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proceedings of the Royal Society of Edinburgh: Section A Mathematics"],"published-print":{"date-parts":[[2004,6]]},"abstract":"<jats:p>We rigorously approach the Schr\u00f6dinger equation of derivative type <jats:italic>q<jats:sub>t<\/jats:sub><\/jats:italic> + i<jats:italic>q<jats:sub>xx<\/jats:sub><\/jats:italic> + \u03bb |<jats:italic>q<\/jats:italic>|<jats:sup>2<\/jats:sup><jats:italic>q<jats:sub>x<\/jats:sub><\/jats:italic> + \u03bc<jats:italic>q<\/jats:italic><jats:sup>2<\/jats:sup><jats:italic>q\u0304<jats:sub>x<\/jats:sub><\/jats:italic> = 0, \u03bb \u2208 R, \u03bc \u2208 C, by the cubic nonlinear Schr\u00f6dinger equation <jats:italic>A<jats:sub>T<\/jats:sub><\/jats:italic> + i <jats:italic>A<jats:sub>XX<\/jats:sub><\/jats:italic> + i <jats:italic>k<\/jats:italic><jats:sub>0<\/jats:sub> (\u03bb \u2212 \u03bc) |<jats:italic>A<\/jats:italic>|<jats:sup>2<\/jats:sup><jats:italic>A<\/jats:italic> = 0. We also study the case of the KdV-like equation <jats:italic>q<jats:sub>t<\/jats:sub><\/jats:italic> + i <jats:italic>q<jats:sub>xx<\/jats:sub><\/jats:italic> + <jats:italic>aq<jats:sub>xxx<\/jats:sub><\/jats:italic> + i |<jats:italic>q<\/jats:italic>|<jats:sup>2<\/jats:sup><jats:italic>q<\/jats:italic> + \u03bb\u0303 (|<jats:italic>q<\/jats:italic>|<jats:sup>2<\/jats:sup><jats:italic>q<\/jats:italic>)<jats:italic><jats:sub>x<\/jats:sub><\/jats:italic> + \u03bc\u0303 |<jats:italic>q<\/jats:italic>|<jats:sup>2<\/jats:sup><jats:italic>q<jats:sub>x<\/jats:sub><\/jats:italic> = 0, \u03bb\u0303 \u03bc\u0303 \u2208 R, arising in optical physics.<\/jats:p>","DOI":"10.1017\/s030821050000336x","type":"journal-article","created":{"date-parts":[[2007,7,16]],"date-time":"2007-07-16T10:51:57Z","timestamp":1184583117000},"page":"595-607","source":"Crossref","is-referenced-by-count":0,"title":["Approximation of the DNLS equation by the cubic nonlinear Schr\u00f6dinger equation"],"prefix":"10.1017","volume":"134","author":[{"given":"Filipe","family":"Oliveira","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2007,7,12]]},"container-title":["Proceedings of the Royal Society of Edinburgh: Section A Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S030821050000336X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,7]],"date-time":"2019-04-07T20:03:02Z","timestamp":1554667382000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S030821050000336X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,6]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2004,6]]}},"alternative-id":["S030821050000336X"],"URL":"https:\/\/doi.org\/10.1017\/s030821050000336x","relation":{},"ISSN":["0308-2105","1473-7124"],"issn-type":[{"value":"0308-2105","type":"print"},{"value":"1473-7124","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,6]]}}}