On the decoupling of the improved Boussinesq equation into two uncoupled Camassa-Holm equations
dc.contributor.author | Erbay, Hüsnü Ata | |
dc.contributor.author | Erbay, Saadet | |
dc.contributor.author | Erkip, A. | |
dc.date.accessioned | 2017-05-02T10:52:46Z | |
dc.date.available | 2017-05-02T10:52:46Z | |
dc.date.issued | 2017-06 | |
dc.identifier.issn | 1553-5231 | en_US |
dc.identifier.uri | http://hdl.handle.net/10679/5046 | |
dc.identifier.uri | https://aimsciences.org/journals/displayArticles.jsp?paperID=13793 | |
dc.description.abstract | We 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.iso | eng | en_US |
dc.publisher | American Institute of Mathematical Sciences | en_US |
dc.relation.ispartof | Discrete and Continuous Dynamical Systems - Series A | en_US |
dc.rights | restrictedAccess | |
dc.title | On the decoupling of the improved Boussinesq equation into two uncoupled Camassa-Holm equations | en_US |
dc.type | Article | en_US |
dc.peerreviewed | yes | en_US |
dc.publicationstatus | published | en_US |
dc.contributor.department | Özyeğin 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.ozuauthor | Erbay, Hüsnü Ata | |
dc.contributor.ozuauthor | Erbay, Saadet | |
dc.identifier.volume | 37 | en_US |
dc.identifier.issue | 6 | en_US |
dc.identifier.startpage | 3111 | en_US |
dc.identifier.endpage | 3122 | en_US |
dc.identifier.wos | WOS:000395905000009 | |
dc.identifier.doi | 10.3934/dcds.2017133 | |
dc.subject.keywords | Camassa-Holm equation | en_US |
dc.subject.keywords | Improved Boussinesq equation | en_US |
dc.subject.keywords | Nonlocal wave equation | en_US |
dc.subject.keywords | Rigorous justification | en_US |
dc.identifier.scopus | SCOPUS:2-s2.0-85017559591 | |
dc.contributor.authorMale | 1 | |
dc.contributor.authorFemale | 1 | |
dc.relation.publicationcategory | Article - International Refereed Journal - Institutional Academic Staff |
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