Re-visiting the head-on collision problem between two solitary waves in shallow water

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dc.authorid0000-0002-3714-6092
dc.authorid0000-0001-8590-3396
dc.contributor.authorÖzden, Ali Erinçen_US
dc.contributor.authorDemiray, Hilmien_US
dc.date.accessioned2015-07-14T11:00:06Z
dc.date.available2015-07-14T11:00:06Z
dc.date.issued2015-03
dc.departmentIşık Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümüen_US
dc.departmentIşık University, Faculty of Arts and Sciences, Department of Mathematicsen_US
dc.description.abstractUpon discovering the wrongness of the statement "although this term does not cause any secularity for this order it will cause secularity at higher order expansion, therefore, that term must vanish" by Su and Mirie [4], in the present work, we studied the head-on collision of two solitary waves propagating in shallow water by introducing a set of stretched coordinates in which the trajectory functions are of order of epsilon(2), where epsilon is the smallness parameter measuring non-linearity. Expanding the field variables and trajectory functions into power series in epsilon, we obtained a set of differential equations governing various terms in the perturbation expansion. By solving them under non-secularity condition we obtained the evolution equations and also the expressions for phase functions. By seeking a progressive wave solution to these evolution equations we have determined the speed correction terms and the phase shifts. As opposed to the result of Su and Mine [4] and similar works, our calculations show that the phase shifts depend on both amplitudes of the colliding waves.en_US
dc.description.versionPublisher's Versionen_US
dc.description.versionAuthor Post Printen_US
dc.identifier.citationÖzden, A. E. & Demiray, H. (2015). Re-visiting the head-on collision problem between two solitary waves in shallow water. International Journal of Non-Linear Mechanics, 69, 66-70. doi:10.1016/j.ijnonlinmec.2014.11.022en_US
dc.identifier.doi10.1016/j.ijnonlinmec.2014.11.022
dc.identifier.endpage70
dc.identifier.issn0020-7462
dc.identifier.issn1878-5638
dc.identifier.scopus2-s2.0-84921328614
dc.identifier.scopusqualityQ1
dc.identifier.startpage66
dc.identifier.urihttps://hdl.handle.net/11729/579
dc.identifier.urihttp://dx.doi.org/10.1016/j.ijnonlinmec.2014.11.022
dc.identifier.volume69
dc.identifier.wosWOS:000349499100007
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.indekslendigikaynakSocial Sciences Citation Index (SSCI)en_US
dc.institutionauthorÖzden, Ali Erinçen_US
dc.institutionauthorDemiray, Hilmien_US
dc.institutionauthorid0000-0002-3714-6092
dc.institutionauthorid0000-0001-8590-3396
dc.language.isoenen_US
dc.peerreviewedYesen_US
dc.publicationstatusPublisheden_US
dc.publisherPergamon-Elsevier Science Ltden_US
dc.relation.ispartofInternational Journal Of Non-Linear Mechanicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectHead-on collisionen_US
dc.subjectSolitary waves in wateren_US
dc.subjectPhase shiftsen_US
dc.subjectFluiden_US
dc.subjectKorteweg-de Vries equationen_US
dc.subjectSolitonsen_US
dc.subjectWater wavesen_US
dc.subjectDifferential equationsen_US
dc.subjectPhase shiften_US
dc.subjectCorrection termsen_US
dc.subjectEvolution equationsen_US
dc.subjectHigher order expansionsen_US
dc.subjectParameter measuringen_US
dc.subjectPerturbation expansionsen_US
dc.subjectProgressive wave solutionsen_US
dc.subjectTrajectory functionsen_US
dc.titleRe-visiting the head-on collision problem between two solitary waves in shallow wateren_US
dc.typeArticleen_US
dspace.entity.typePublication

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