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General soliton matrices in the Riemann-Hilbert problem for integrable nonlinear equations

dc.contributor.authorShchesnovich, V. S.
dc.contributor.authorYang, J. K.
dc.contributor.institutionUniv Vermont
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.date.accessioned2014-05-20T14:08:11Z
dc.date.available2014-05-20T14:08:11Z
dc.date.issued2003-10-01
dc.description.abstractWe derive the soliton matrices corresponding to an arbitrary number of higher-order normal zeros for the matrix Riemann-Hilbert problem of arbitrary matrix dimension, thus giving the complete solution to the problem of higher-order solitons. Our soliton matrices explicitly give all higher-order multisoliton solutions to the nonlinear partial differential equations integrable through the matrix Riemann-Hilbert problem. We have applied these general results to the three-wave interaction system, and derived new classes of higher-order soliton and two-soliton solutions, in complement to those from our previous publication [Stud. Appl. Math. 110, 297 (2003)], where only the elementary higher-order zeros were considered. The higher-order solitons corresponding to nonelementary zeros generically describe the simultaneous breakup of a pumping wave (u(3)) into the other two components (u(1) and u(2)) and merger of u(1) and u(2) waves into the pumping u(3) wave. The two-soliton solutions corresponding to two simple zeros generically describe the breakup of the pumping u(3) wave into the u(1) and u(2) components, and the reverse process. In the nongeneric cases, these two-soliton solutions could describe the elastic interaction of the u(1) and u(2) waves, thus reproducing previous results obtained by Zakharov and Manakov [Zh. Eksp. Teor. Fiz. 69, 1654 (1975)] and Kaup [Stud. Appl. Math. 55, 9 (1976)]. (C) 2003 American Institute of Physics.en
dc.description.affiliationUniv Vermont, Dept Math & Stat, Burlington, VT 05401 USA
dc.description.affiliationUniv Estadual Paulista, Inst Fis Teor, BR-01405900 São Paulo, Brazil
dc.description.affiliationUnespUniv Estadual Paulista, Inst Fis Teor, BR-01405900 São Paulo, Brazil
dc.format.extent4604-4639
dc.identifierhttp://dx.doi.org/10.1063/1.1605821
dc.identifier.citationJournal of Mathematical Physics. Melville: Amer Inst Physics, v. 44, n. 10, p. 4604-4639, 2003.
dc.identifier.doi10.1063/1.1605821
dc.identifier.fileWOS000185421900013.pdf
dc.identifier.issn0022-2488
dc.identifier.urihttp://hdl.handle.net/11449/23918
dc.identifier.wosWOS:000185421900013
dc.language.isoeng
dc.publisherAmerican Institute of Physics (AIP)
dc.relation.ispartofJournal of Mathematical Physics
dc.relation.ispartofjcr1.165
dc.relation.ispartofsjr0,644
dc.rights.accessRightsAcesso aberto
dc.sourceWeb of Science
dc.titleGeneral soliton matrices in the Riemann-Hilbert problem for integrable nonlinear equationsen
dc.typeArtigo
dcterms.licensehttp://publishing.aip.org/authors/web-posting-guidelines
dcterms.rightsHolderAmer Inst Physics
dspace.entity.typePublication
unesp.campusUniversidade Estadual Paulista (UNESP), Instituto de Física Teórica (IFT), São Paulopt

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