dc.contributor.author Béthuel, Fabrice dc.contributor.author Gravejat, Philippe HAL ID: 812 dc.contributor.author Saut, Jean-Claude dc.contributor.author Smets, Didier dc.date.accessioned 2010-02-15T10:40:34Z dc.date.available 2010-02-15T10:40:34Z dc.date.issued 2010 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/3453 dc.language.iso en en dc.subject Gross-Pitaevskii equation en dc.subject Korteweg-de Vries equation en dc.subject long-wave limit en dc.subject.ddc 515 en dc.title On the Korteweg-de Vries long-wave approximation of the Gross-Pitaevskii equation II en dc.type Article accepté pour publication ou publié dc.description.abstracten In this paper, we proceed along our analysis of the Korteweg-de Vries approximation of the Gross-Pitaevskii equation initiated in a previous paper. At the long-wave limit, we establish that solutions of small amplitude to the one-dimensional Gross-Pitaevskii equation split into two waves with opposite constant speeds $\pm \sqrt{2}$, each of which are solutions to a Korteweg-de Vries equation. We also compute an estimate of the error term which is somewhat optimal as long as travelling waves are considered. At the cost of higher regularity of the initial data, this improves our previous estimate. en dc.relation.isversionofjnlname Communications in Partial Differential Equations dc.relation.isversionofjnlvol 35 en dc.relation.isversionofjnlissue 1 en dc.relation.isversionofjnldate 2010-01 dc.relation.isversionofjnlpages 113-164 en dc.relation.isversionofdoi http://dx.doi.org/10.1080/03605300903222542 en dc.identifier.urlsite http://hal.archives-ouvertes.fr/hal-00371344/en/ en dc.description.sponsorshipprivate oui en dc.relation.isversionofjnlpublisher Taylor & Francis en dc.subject.ddclabel Analyse en
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