A numerical study of the large-period limit of a Zakharov-Shabat eigenvalue problem with periodic potentials

dc.contributor.authorOlivier, C P
dc.contributor.authorHerbst, B M
dc.contributor.authorMolchan, M A
dc.date.accessioned2016-08-11T14:24:25Z
dc.date.available2016-08-11T14:24:25Z
dc.date.issued2012
dc.date.updated2016-08-11T13:49:26Z
dc.description.abstractDeconinck and Kutz (2006 J. Comput. Phys. 219 296–321) developed an efficient algorithm for solving the Zakharov–Shabat eigenvalue problem with periodic potentials numerically. It is natural to use the same algorithm for solving the problem for non-periodic potential (decaying potentials defined over the whole real line) using large periods. In this paper, we propose the use of a specific value of the Floquet exponent. Our numerical results indicate that it can produce accurate results long before the period becomes large enough for the analytical convergence results of Gardner (1997 J. Reine Angew. Math. 491 149–81) to be valid. We also illustrate the rather complicated path to convergence of some nonlinear Schrodinger potentials. ¨ PACS numbers: 02.30.Ik, 02.60.−x, 05.45.Yven_ZA
dc.identifier.apacitationOlivier, C. P., Herbst, B. M., & Molchan, M. A. (2012). A numerical study of the large-period limit of a Zakharov-Shabat eigenvalue problem with periodic potentials. <i>Journal of Physics A: Mathematical and Theoretical</i>, http://hdl.handle.net/11427/21200en_ZA
dc.identifier.chicagocitationOlivier, C P, B M Herbst, and M A Molchan "A numerical study of the large-period limit of a Zakharov-Shabat eigenvalue problem with periodic potentials." <i>Journal of Physics A: Mathematical and Theoretical</i> (2012) http://hdl.handle.net/11427/21200en_ZA
dc.identifier.citationOlivier, C. P., Herbst, B. M., & Molchan, M. A. (2012). A numerical study of the large-period limit of a Zakharov–Shabat eigenvalue problem with periodic potentials. Journal of Physics A: Mathematical and Theoretical, 45(25), 255205.en_ZA
dc.identifier.issn1751-8113en_ZA
dc.identifier.ris TY - Journal Article AU - Olivier, C P AU - Herbst, B M AU - Molchan, M A AB - Deconinck and Kutz (2006 J. Comput. Phys. 219 296–321) developed an efficient algorithm for solving the Zakharov–Shabat eigenvalue problem with periodic potentials numerically. It is natural to use the same algorithm for solving the problem for non-periodic potential (decaying potentials defined over the whole real line) using large periods. In this paper, we propose the use of a specific value of the Floquet exponent. Our numerical results indicate that it can produce accurate results long before the period becomes large enough for the analytical convergence results of Gardner (1997 J. Reine Angew. Math. 491 149–81) to be valid. We also illustrate the rather complicated path to convergence of some nonlinear Schrodinger potentials. ¨ PACS numbers: 02.30.Ik, 02.60.−x, 05.45.Yv DA - 2012 DB - OpenUCT DP - University of Cape Town J1 - Journal of Physics A: Mathematical and Theoretical LK - https://open.uct.ac.za PB - University of Cape Town PY - 2012 SM - 1751-8113 T1 - A numerical study of the large-period limit of a Zakharov-Shabat eigenvalue problem with periodic potentials TI - A numerical study of the large-period limit of a Zakharov-Shabat eigenvalue problem with periodic potentials UR - http://hdl.handle.net/11427/21200 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/21200
dc.identifier.vancouvercitationOlivier CP, Herbst BM, Molchan MA. A numerical study of the large-period limit of a Zakharov-Shabat eigenvalue problem with periodic potentials. Journal of Physics A: Mathematical and Theoretical. 2012; http://hdl.handle.net/11427/21200.en_ZA
dc.languageengen_ZA
dc.publisherIOP Publishingen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.sourceJournal of Physics A: Mathematical and Theoreticalen_ZA
dc.source.urihttp://iopscience.iop.org/journal/0305-4470
dc.titleA numerical study of the large-period limit of a Zakharov-Shabat eigenvalue problem with periodic potentialsen_ZA
dc.typeJournal Articleen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceArticleen_ZA
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