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dc.contributor.authorRemonato, Filippo
dc.contributor.authorKalisch, Henrik
dc.date.accessioned2017-12-19T10:55:00Z
dc.date.available2017-12-19T10:55:00Z
dc.date.issued2017-03
dc.PublishedRemonato F, Kalisch H. Numerical bifurcation for the capillary Whitham equation. Physica D : Non-linear Phenomena. 2017;343:51-62eng
dc.identifier.issn0167-2789en_US
dc.identifier.issn1872-8022en_US
dc.identifier.urihttps://hdl.handle.net/1956/17040
dc.description.abstractThe so-called Whitham equation arises in the modeling of free surface water waves, and combines a generic nonlinear quadratic term with the exact linear dispersion relation for gravity waves on the free surface of a fluid with finite depth. In this work, the effect of incorporating capillarity into the Whitham equation is in focus. The capillary Whitham equation is a nonlocal equation similar to the usual Whitham equation, but containing an additional term with a coefficient depending on the Bond number which measures the relative strength of capillary and gravity effects on the wave motion. A spectral collocation scheme for computing approximations to periodic traveling waves for the capillary Whitham equation is put forward. Numerical approximations of periodic traveling waves are computed using a bifurcation approach, and a number of bifurcation curves are found. Our analysis uncovers a rich structure of bifurcation patterns, including subharmonic bifurcations, as well as connecting and crossing branches. Indeed, for some values of the Bond number, the bifurcation diagram features distinct branches of solutions which intersect at a secondary bifurcation point. The same branches may also cross without connecting, and some bifurcation curves feature self-crossings without self-connections.en_US
dc.language.isoengeng
dc.publisherElsevieren_US
dc.relation.urihttp://www.sciencedirect.com/science/article/pii/S0167278916302135
dc.subjectWhitham equationeng
dc.subjectCapillarityeng
dc.subjectGlobal bifurcationeng
dc.subjectSpectral projectioneng
dc.subjectPseudo-arclength parametrizationeng
dc.titleNumerical bifurcation for the capillary Whitham equationen_US
dc.typeJournal article
dc.date.updated2017-11-28T13:39:34Z
dc.description.versionsubmittedVersionen_US
dc.rights.holderCopyright the Author(s)en_US
dc.identifier.doihttps://doi.org/10.1016/j.physd.2016.11.003
dc.identifier.cristin1447737
dc.source.journalPhysica D : Non-linear Phenomena
dc.relation.projectNorges forskningsråd: 231668
dc.relation.projectNorges forskningsråd: 213474/F20
dc.subject.nsiVDP::Matematikk og naturvitenskap: 400::Matematikk: 410
dc.subject.nsiVDP::Mathematics and natural scienses: 400::Mathematics: 410


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