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dc.contributorThe Pennsylvania State University CiteSeerX Archives
dc.date.accessioned2019-10-24T19:20:34Z
dc.date.available2019-10-24T19:20:34Z
dc.date.created2017-02-28 01:24
dc.date.issued2016-08-18
dc.identifieroai:CiteSeerX.psu:10.1.1.768.9152
dc.identifierhttp://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.768.9152
dc.identifier.urihttp://hdl.handle.net/20.500.12424/1031929
dc.description.abstractWe consider the initial-value problem for a system of coupled Boussinesq equations on the infinite line for localised or sufficiently rapidly decaying initial data, generating sufficiently rapidly decaying right- and left-propagating waves. We study the dynamics of weakly nonlinear waves, and using asymptotic multiple-scales expansions and averaging with respect to the fast time, we obtain a hierarchy of asymptotically exact coupled and uncoupled Ostrovsky equations for unidirectional waves. We then construct a weakly nonlinear solution of the initial-value problem in terms of solutions of the derived Ostrovsky equations within the accuracy of the governing equations, and show that there are no secular terms. When coupling parameters are equal to zero, our results yield a weakly nonlinear solution of the initial-value problem for the Boussinesq equation in terms of solutions of the initial-value problems for two Korteweg-de Vries equations, integrable by the Inverse Scattering Transform. We also perform relevant numerical simulations of the original unapproximated system of Boussinesq equations to illustrate the difference in the behaviour of its solutions for different asymptotic regimes.
dc.format.mediumapplication/pdf
dc.languageen
dc.language.isoeng
dc.rightsMetadata may be used without restrictions as long as the oai identifier remains attached to it.
dc.subjectCoupled Boussinesq equations
dc.subjectOstrovsky equation
dc.subjectAsymptotic multiple-scales expansions
dc.subjectAveraging
dc.subjectInitial-value problem
dc.titleInitial-value problem for coupled Boussinesq equations and
dc.typetext
ge.collectioncodeOAIDATA
ge.dataimportlabelOAI metadata object
ge.identifier.legacyglobethics:10670926
ge.identifier.permalinkhttps://www.globethics.net/gtl/10670926
ge.lastmodificationdate2017-02-28 01:24
ge.lastmodificationuseradmin@pointsoftware.ch (import)
ge.submissions0
ge.oai.exportid149001
ge.oai.repositoryid54
ge.oai.streamid5
ge.setnameGlobeTheoLib
ge.setspecglobetheolib
ge.linkhttp://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.768.9152
ge.linkhttp://arxiv.org/pdf/1104.3432.pdf


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