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dc.contributor.authorErbay, Hüsnü Ata
dc.contributor.authorErbay, Saadet
dc.contributor.authorErkip, A.
dc.date.accessioned2016-12-06T18:32:36Z
dc.date.available2016-12-06T18:32:36Z
dc.date.issued2016-11
dc.identifier.issn1553-5231
dc.identifier.urihttp://hdl.handle.net/10679/4568
dc.identifier.urihttps://www.aimsciences.org/journals/displayArticles.jsp?paperID=12898
dc.description.abstractIn the present study we prove rigorously that in the long-wave limit, the unidirectional solutions of a class of nonlocal wave equations to which the improved Boussinesq equation belongs are well approximated by the solutions of the Camassa-Holm equation over a long time scale. This general class of nonlocal wave equations model bidirectional wave propagation in a nonlocally and nonlinearly elastic medium whose constitutive equation is given by a convolution integral. To justify the Camassa-Holm approximation we show that approximation errors remain small over a long time interval. To be more precise, we obtain error estimates in terms of two independent, small, positive parameters \epsilon and \delta measuring the effect of nonlinearity and dispersion, respectively. We further show that similar conclusions are also valid for the lower order approximations: the Benjamin-Bona-Mahony approximation and the Korteweg-de Vries approximation.
dc.language.isoengen_US
dc.publisherAIMS
dc.relation.ispartofDiscrete And Continuous Dynamical Systems
dc.rightsrestrictedAccess
dc.titleThe Camassa-Holm equation as the long-wave limit of the improved Boussinesq equation and of a class of nonlocal wave equationsen_US
dc.typeArticleen_US
dc.peerreviewedyes
dc.publicationstatuspublished
dc.contributor.departmentÖzyeğin University
dc.contributor.authorID119316
dc.contributor.authorID119313
dc.contributor.ozuauthorErbay, Hüsnü Ata
dc.contributor.ozuauthorErbay, Saadet
dc.identifier.wosWOS:000385221300010
dc.identifier.doi10.3934/dcds.2016066
dc.subject.keywordsCamassa-Holm equation
dc.subject.keywordsImproved Boussinesq equation
dc.subject.keywordsNonlocal wave equation
dc.subject.keywordsRigorous justification
dc.identifier.scopusSCOPUS:2-s2.0-84984870611
dc.contributor.authorMale1
dc.contributor.authorFemale1


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