Unidirectional wave motion in a nonlocally and nonlinearly elastic medium: The KdV, BBM and CH equations
dc.contributor.author | Erbay, Hüsnü Ata | |
dc.contributor.author | Erbay, Saadet | |
dc.contributor.author | Erkip, A. | |
dc.date.accessioned | 2015-10-26T14:07:43Z | |
dc.date.available | 2015-10-26T14:07:43Z | |
dc.date.issued | 2015 | |
dc.identifier.uri | http://hdl.handle.net/10679/976 | |
dc.identifier.uri | http://www.kirj.ee/26185/?tpl=1061&c_tpl=1064 | |
dc.description.abstract | We consider unidirectional wave propagation in a nonlocally and nonlinearly elastic medium whose constitutive equation is given by a convolution integral with a suitable kernel function. We first give a brief review of asymptotic wave models describing the unidirectional propagation of small-but-finite amplitude long waves. When the kernel function is the well-known exponential kernel, the asymptotic description is provided by the Korteweg–de Vries (KdV) equation, the Benjamin–Bona–Mahony (BBM) equation, or the Camassa–Holm (CH) equation. When the Fourier transform of the kernel function has fractional powers, it turns out that fractional forms of these equations describe unidirectional propagation of the waves. We then compare the exact solutions of the KdV equation and the BBM equation with the numerical solutions of the nonlocal model. We observe that the solution of the nonlocal model is well approximated by associated solutions of the KdV equation and the BBM equation over the time interval considered. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Estonian Academy of Sciences | en_US |
dc.relation.ispartof | Proceedings of the Estonian Academy of Sciences | |
dc.rights | openAccess | |
dc.title | Unidirectional wave motion in a nonlocally and nonlinearly elastic medium: The KdV, BBM and CH equations | en_US |
dc.type | Conference paper | en_US |
dc.description.version | publisher version | |
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 | 64 | |
dc.identifier.issue | 3 | |
dc.identifier.startpage | 256 | |
dc.identifier.endpage | 262 | |
dc.identifier.wos | WOS:000360140700009 | |
dc.identifier.doi | 10.3176/proc.2015.3.08 | |
dc.subject.keywords | nonlocal elasticity | en_US |
dc.subject.keywords | Korteweg–de Vries equation | en_US |
dc.subject.keywords | Benjamin–Bona–Mahony equation | en_US |
dc.subject.keywords | Camassa–Holm equation | en_US |
dc.subject.keywords | fractional Camassa–Holm equation | en_US |
dc.identifier.scopus | SCOPUS:2-s2.0-84947804639 | |
dc.contributor.authorMale | 1 | |
dc.contributor.authorFemale | 1 | |
dc.relation.publicationcategory | Conference Paper - International - Institutional Academic Staff |
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