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dc.contributor.authorKraenkel, Roberto André-
dc.contributor.authorPereira, J. G.-
dc.contributor.authorManna, M. A.-
dc.date.accessioned2014-05-20T15:21:11Z-
dc.date.accessioned2016-10-25T17:54:32Z-
dc.date.available2014-05-20T15:21:11Z-
dc.date.available2016-10-25T17:54:32Z-
dc.date.issued1995-06-01-
dc.identifierhttp://dx.doi.org/10.1007/BF00994645-
dc.identifier.citationActa Applicandae Mathematicae. Dordrecht: Kluwer Academic Publ, v. 39, n. 1-3, p. 389-403, 1995.-
dc.identifier.issn0167-8019-
dc.identifier.urihttp://hdl.handle.net/11449/32358-
dc.identifier.urihttp://acervodigital.unesp.br/handle/11449/32358-
dc.description.abstractBy using the reductive perturbation method of Taniuti with the introduction of an infinite sequence of slow time variables tau(1), tau(3), tau(5), ..., we study the propagation of long surface-waves in a shallow inviscid fluid. The Korteweg-de Vries (KdV) equation appears as the lowest order amplitude equation in slow variables. In this context, we show that, if the lowest order wave amplitude zeta(0) satisfies the KdV equation in the time tau(3), it must satisfy the (2n+1)th order equation of the KdV hierarchy in the time tau(2n+1), With n = 2, 3, 4,.... AS a consequence of this fact, we show with an explicit example that the secularities of the evolution equations for the higher-order terms (zeta(1), zeta(2),...) of the amplitude can be eliminated when zeta(0) is a solitonic solution to the KdV equation. By reversing this argument, we can say that the requirement of a secular-free perturbation theory implies that the amplitude zeta(0) satisfies the (2n+1)th order equation of the KdV hierarchy in the time tau(2n+1) This essentially means that the equations of the KdV hierarchy do play a role in perturbation theory. Thereafter, by considering a solitary-wave solution, we show, again with an explicit, example that the elimination of secularities through the use of the higher order KdV hierarchy equations corresponds, in the laboratory coordinates, to a renormalization of the solitary-wave velocity. Then, we conclude that this procedure of eliminating secularities is closely related to the renormalization technique developed by Kodama and Taniuti.en
dc.format.extent389-403-
dc.language.isoeng-
dc.publisherKluwer Academic Publ-
dc.sourceWeb of Science-
dc.subjectREDUCTIVE PERTURBATION METHODpt
dc.subjectMULTIPLE TIME FORMALISMpt
dc.subjectHIGHER-ORDER EVOLUTION EQUATIONSpt
dc.titleTHE REDUCTIVE PERTURBATION METHOD AND THE KORTEWEG-DE VRIES HIERARCHYen
dc.typeoutro-
dc.contributor.institutionUniversidade Estadual Paulista (UNESP)-
dc.contributor.institutionUNIV MONTPELLIER 2-
dc.description.affiliationUNIV ESTADUAL PAULISTA,INST FIS TEOR,BR-01405900 SAO PAULO,BRAZIL-
dc.description.affiliationUNIV MONTPELLIER 2,F-34095 MONTPELLIER,FRANCE-
dc.description.affiliationUnespUNIV ESTADUAL PAULISTA,INST FIS TEOR,BR-01405900 SAO PAULO,BRAZIL-
dc.identifier.doi10.1007/BF00994645-
dc.identifier.wosWOS:A1995QW85700023-
dc.rights.accessRightsAcesso restrito-
dc.relation.ispartofActa Applicandae Mathematicae-
Appears in Collections:Artigos, TCCs, Teses e Dissertações da Unesp

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