dc.contributor.author Erbay, Hüsnü Ata dc.contributor.author Erbay, Saadet dc.contributor.author Erkip, A. dc.date.accessioned 2016-12-06T18:32:36Z dc.date.available 2016-12-06T18:32:36Z dc.date.issued 2016-11 dc.identifier.issn 1553-5231 dc.identifier.uri http://hdl.handle.net/10679/4568 dc.identifier.uri https://www.aimsciences.org/journals/displayArticles.jsp?paperID=12898 dc.description.abstract In 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.iso eng en_US dc.publisher AIMS dc.relation.ispartof Discrete And Continuous Dynamical Systems dc.rights restrictedAccess dc.title The Camassa-Holm equation as the long-wave limit of the improved Boussinesq equation and of a class of nonlocal wave equations en_US dc.type Article en_US dc.peerreviewed yes dc.publicationstatus published dc.contributor.department Özyeğin University dc.contributor.authorID 119316 dc.contributor.authorID 119313 dc.contributor.ozuauthor Erbay, Hüsnü Ata dc.contributor.ozuauthor Erbay, Saadet dc.identifier.wos WOS:000385221300010 dc.identifier.doi 10.3934/dcds.2016066 dc.subject.keywords Camassa-Holm equation dc.subject.keywords Improved Boussinesq equation dc.subject.keywords Nonlocal wave equation dc.subject.keywords Rigorous justification dc.identifier.scopus SCOPUS:2-s2.0-84984870611 dc.contributor.authorMale 1 dc.contributor.authorFemale 1
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