Some remarks on the stability and instability properties of solitary waves for the double dispersion equation
dc.contributor.author | Erbay, Hüsnü Ata | |
dc.contributor.author | Erbay, Saadet | |
dc.contributor.author | Erkip, A. | |
dc.date.accessioned | 2015-10-26T13:35:24Z | |
dc.date.available | 2015-10-26T13:35:24Z | |
dc.date.issued | 2015 | |
dc.identifier.uri | http://hdl.handle.net/10679/975 | |
dc.identifier.uri | http://www.kirj.ee/26179/?tpl=1061&c_tpl=1064 | |
dc.description.abstract | In this article we give a review of our recent results on the instability and stability properties of travelling wave solutions of the double dispersion equation utt − uxx + auxxxx − buxxtt = −(|u|p−1u)xx for p > 1, a ≥ b > 0. After a brief reminder of the general class of nonlocal wave equations to which the double dispersion equation belongs, we summarize our findings for both the existence and orbital stability/instability of travelling wave solutions to the general class of nonlocal wave equations. We then state (i) the conditions under which travelling wave solutions of the double dispersion equation are unstable by blow-up and (ii) the conditions under which the travelling waves are orbitally stable. We plot the instability/stability regions in the plane defined by wave velocity and the quotient b/a for various values of p. | 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 | Some remarks on the stability and instability properties of solitary waves for the double dispersion equation | 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 | 263 | |
dc.identifier.endpage | 269 | |
dc.identifier.wos | WOS:000360140700010 | |
dc.identifier.doi | 10.3176/proc.2015.3.09 | |
dc.subject.keywords | Double dispersion equation | en_US |
dc.subject.keywords | Boussinesq equation | en_US |
dc.subject.keywords | Solitary waves | en_US |
dc.subject.keywords | Instability by blow-up | en_US |
dc.subject.keywords | Orbital stability | en_US |
dc.subject.keywords | Travelling waves | en_US |
dc.identifier.scopus | SCOPUS:2-s2.0-84939511087 | |
dc.contributor.authorMale | 1 | |
dc.contributor.authorFemale | 1 | |
dc.relation.publicationcategory | Conference Paper - International - Institutional Academic Staff |
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