The algebraic structure behind the derivative nonlinear Schrödinger equation

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dc.contributor.authorFrança, G. S. [UNESP]
dc.contributor.authorGomes, J. F. [UNESP]
dc.contributor.authorZimerman, A. H. [UNESP]
dc.contributor.institutionCornell University
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.date.accessioned2014-05-27T11:30:07Z
dc.date.available2014-05-27T11:30:07Z
dc.date.issued2013-08-02
dc.description.abstractThe Kaup-Newell (KN) hierarchy contains the derivative nonlinear Schrödinger equation (DNLSE) amongst others interesting and important nonlinear integrable equations. In this paper, a general higher grading affine algebraic construction of integrable hierarchies is proposed and the KN hierarchy is established in terms of an Ŝℓ2Kac-Moody algebra and principal gradation. In this form, our spectral problem is linear in the spectral parameter. The positive and negative flows are derived, showing that some interesting physical models arise from the same algebraic structure. For instance, the DNLSE is obtained as the second positive, while the Mikhailov model as the first negative flows. The equivalence between the latter and the massive Thirring model is also explicitly demonstrated. The algebraic dressing method is employed to construct soliton solutions in a systematic manner for all members of the hierarchy. Finally, the equivalence of the spectral problem introduced in this paper with the usual one, which is quadratic in the spectral parameter, is achieved by setting a particular automorphism of the affine algebra, which maps the homogeneous into principal gradation. © 2013 IOP Publishing Ltd.en
dc.description.affiliationDepartment of Physics Cornell University, Ithaca, NY
dc.description.affiliationInstituto de Física Teórica-IFT UNESP, São Paulo, SP
dc.description.affiliationUnespInstituto de Física Teórica-IFT UNESP, São Paulo, SP
dc.identifierhttp://dx.doi.org/10.1088/1751-8113/46/30/305201
dc.identifier.citationJournal of Physics A: Mathematical and Theoretical, v. 46, n. 30, 2013.
dc.identifier.doi10.1088/1751-8113/46/30/305201
dc.identifier.issn1751-8113
dc.identifier.issn1751-8121
dc.identifier.lattes9287776078149551
dc.identifier.lattes8215976645016606
dc.identifier.scopus2-s2.0-84880368308
dc.identifier.urihttp://hdl.handle.net/11449/76210
dc.identifier.wosWOS:000321569900005
dc.language.isoeng
dc.relation.ispartofJournal of Physics A: Mathematical and Theoretical
dc.relation.ispartofjcr1.963
dc.relation.ispartofsjr0,843
dc.relation.ispartofsjr0,843
dc.rights.accessRightsAcesso restrito
dc.sourceScopus
dc.titleThe algebraic structure behind the derivative nonlinear Schrödinger equationen
dc.typeArtigo
dcterms.licensehttp://iopscience.iop.org/page/copyright
unesp.author.lattes9287776078149551
unesp.author.lattes8215976645016606[3]
unesp.campusUniversidade Estadual Paulista (Unesp), Instituto de Física Teórica (IFT), São Paulopt

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