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dc.contributor.authorErbay, Hüsnü Ata
dc.contributor.authorErbay, Saadet
dc.contributor.authorErkip, A.
dc.date.accessioned2017-05-02T10:52:46Z
dc.date.available2017-05-02T10:52:46Z
dc.date.issued2017-06
dc.identifier.issn1553-5231en_US
dc.identifier.urihttp://hdl.handle.net/10679/5046
dc.identifier.urihttps://aimsciences.org/journals/displayArticles.jsp?paperID=13793
dc.description.abstractWe rigorously establish that, in the long-wave regime characterized by the assumptions of long wavelength and small amplitude, bidirectional solutions of the improved Boussinesq equation tend to associated solutions of two uncoupled Camassa-Holm equations. We give a precise estimate for approximation errors in terms of two small positive parameters measuring the effects of nonlinearity and dispersion. Our results demonstrate that, in the present regime, any solution of the improved Boussinesq equation is split into two waves propagating in opposite directions independently, each of which is governed by the Camassa-Holm equation. We observe that the approximation error for the decoupled problem considered in the present study is greater than the approximation error for the unidirectional problem characterized by a single Camassa-Holm equation. We also consider lower order approximations and we state similar error estimates for both the Benjamin-Bona-Mahony approximation and the Korteweg-de Vries approximation.en_US
dc.language.isoengen_US
dc.publisherAmerican Institute of Mathematical Sciencesen_US
dc.relation.ispartofDiscrete and Continuous Dynamical Systems - Series Aen_US
dc.rightsrestrictedAccess
dc.titleOn the decoupling of the improved Boussinesq equation into two uncoupled Camassa-Holm equationsen_US
dc.typeArticleen_US
dc.peerreviewedyesen_US
dc.publicationstatuspublisheden_US
dc.contributor.departmentÖzyeğin University
dc.contributor.authorID(ORCID 0000-0002-5167-609X & YÖK ID 119316) Erbay, Hüsnü Ata
dc.contributor.authorID(ORCID 0000-0002-6080-4591 & YÖK ID 119313) Erbay, Saadet
dc.contributor.ozuauthorErbay, Hüsnü Ata
dc.contributor.ozuauthorErbay, Saadet
dc.identifier.volume37en_US
dc.identifier.issue6en_US
dc.identifier.startpage3111en_US
dc.identifier.endpage3122en_US
dc.identifier.wosWOS:000395905000009
dc.identifier.doi10.3934/dcds.2017133
dc.subject.keywordsCamassa-Holm equationen_US
dc.subject.keywordsImproved Boussinesq equationen_US
dc.subject.keywordsNonlocal wave equationen_US
dc.subject.keywordsRigorous justificationen_US
dc.identifier.scopusSCOPUS:2-s2.0-85017559591
dc.contributor.authorMale1
dc.contributor.authorFemale1
dc.relation.publicationcategoryArticle - International Refereed Journal - Institutional Academic Staff


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