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dc.contributor.authorNilsson, Dag Viktor
dc.date.accessioned2020-01-24T10:27:29Z
dc.date.available2020-01-24T10:27:29Z
dc.date.created2019-11-02T14:03:51Z
dc.date.issued2019
dc.identifier.citationMathematical methods in the applied sciences. 2019, 42 (12), 4113-4145.nb_NO
dc.identifier.issn0170-4214
dc.identifier.urihttp://hdl.handle.net/11250/2637789
dc.description.abstractWe consider three‐dimensional inviscid‐irrotational flow in a two‐layer fluid under the effects of gravity and surface tension, where the upper fluid is bounded above by a rigid lid and the lower fluid is bounded below by a flat bottom. We use a spatial dynamics approach and formulate the steady Euler equations as an infinite‐dimensional Hamiltonian system, where an unbounded spatial direction x is considered as a time‐like coordinate. In addition, we consider wave motions that are periodic in another direction z. By analyzing the dispersion relation, we detect several bifurcation scenarios, two of which we study further: a type of 00(is)(iκ0) resonance and a Hamiltonian Hopf bifurcation. The bifurcations are investigated by performing a center‐manifold reduction, which yields a finite‐dimensional Hamiltonian system. For this finite‐dimensional system, we establish the existence of periodic and homoclinic orbits, which correspond to, respectively, doubly periodic travelling waves and oblique travelling waves with a dark or bright solitary wave profile in the x direction. The former are obtained using a variational Lyapunov‐Schmidt reduction and the latter by first applying a normal form transformation and then studying the resulting canonical system of equations.nb_NO
dc.language.isoengnb_NO
dc.publisherWileynb_NO
dc.titleThree-dimensional internal gravity-capillary waves in finite depthnb_NO
dc.typeJournal articlenb_NO
dc.typePeer reviewednb_NO
dc.description.versionacceptedVersionnb_NO
dc.source.pagenumber4113-4145nb_NO
dc.source.volume42nb_NO
dc.source.journalMathematical methods in the applied sciencesnb_NO
dc.source.issue12nb_NO
dc.identifier.doi10.1002/mma.5635
dc.identifier.cristin1743462
dc.description.localcodeLocked until 16.4.2020 due to copyright restrictions. This is the peer reviewed version of an article, which has been published in final form at [https://doi.org/10.1002/mma.5635]. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.nb_NO
cristin.unitcode194,63,15,0
cristin.unitnameInstitutt for matematiske fag
cristin.ispublishedtrue
cristin.fulltextpreprint
cristin.qualitycode1


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