An integrable evolution equation for surface waves in deep water

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dc.contributor.authorKraenkel, R. A. [UNESP]
dc.contributor.authorLeblond, H.
dc.contributor.authorManna, M. A.
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.contributor.institutionUniv Angers
dc.contributor.institutionUniv Montpellier 2
dc.date.accessioned2014-12-03T13:11:22Z
dc.date.available2014-12-03T13:11:22Z
dc.date.issued2014-01-17
dc.description.abstractIn order to describe the dynamics of monochromatic surface waves in deep water, we derive a nonlinear and dispersive system of equations for the free surface elevation and the free surface velocity from the Euler equations in infinite depth. From it, and using a multiscale perturbative method, an asymptotic model for small wave steepness ratio is derived. The model is shown to be completely integrable. The Lax pair, the first conserved quantities as well as the symmetries are exhibited. Theoretical and numerical studies reveal that it supports periodic progressive Stokes waves which peak and break in finite time. Comparison between the limiting wave solution of the asymptotic model and classical results is performed.en
dc.description.affiliationUniv Estadual Paulista UNESP, Inst Fis Teor UNESP, BR-01140070 Sao Paulo, Brazil
dc.description.affiliationUniv Angers, LUNAM Univ, Lab Photon Angers, F-49045 Angers 1, France
dc.description.affiliationUniv Montpellier 2, Lab Charles Coulomb, CNR, UMR 5221, F-34095 Montpellier, France
dc.description.affiliationUnespUniv Estadual Paulista UNESP, Inst Fis Teor UNESP, BR-01140070 Sao Paulo, Brazil
dc.format.extent17
dc.identifierhttp://dx.doi.org/10.1088/1751-8113/47/2/025208
dc.identifier.citationJournal Of Physics A-mathematical And Theoretical. Bristol: Iop Publishing Ltd, v. 47, n. 2, 17 p., 2014.
dc.identifier.doi10.1088/1751-8113/47/2/025208
dc.identifier.issn1751-8113
dc.identifier.urihttp://hdl.handle.net/11449/113045
dc.identifier.wosWOS:000329041500012
dc.language.isoeng
dc.publisherIop Publishing Ltd
dc.relation.ispartofJournal of Physics A: Mathematical and Theoretical
dc.relation.ispartofjcr1.963
dc.relation.ispartofsjr0,843
dc.rights.accessRightsAcesso restrito
dc.sourceWeb of Science
dc.subjectintegrable systemsen
dc.subjectmulti-scale methodsen
dc.subjectdeep wateren
dc.subjectgravity wavesen
dc.titleAn integrable evolution equation for surface waves in deep wateren
dc.typeArtigo
dcterms.licensehttp://iopscience.iop.org/page/copyright
dcterms.rightsHolderIop Publishing Ltd
unesp.campusUniversidade Estadual Paulista (Unesp), Instituto de Física Teórica (IFT), São Paulopt

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