A numerical study of the large-period limit of a Zakharov-Shabat eigenvalue problem with periodic potentials
dc.contributor.author | Olivier, C P | |
dc.contributor.author | Herbst, B M | |
dc.contributor.author | Molchan, M A | |
dc.date.accessioned | 2016-08-11T14:24:25Z | |
dc.date.available | 2016-08-11T14:24:25Z | |
dc.date.issued | 2012 | |
dc.date.updated | 2016-08-11T13:49:26Z | |
dc.description.abstract | 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 | en_ZA |
dc.identifier.apacitation | Olivier, 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/11427/21200 | en_ZA |
dc.identifier.chicagocitation | Olivier, 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/11427/21200 | en_ZA |
dc.identifier.citation | Olivier, 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.issn | 1751-8113 | en_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.uri | http://hdl.handle.net/11427/21200 | |
dc.identifier.vancouvercitation | Olivier 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.language | eng | en_ZA |
dc.publisher | IOP Publishing | en_ZA |
dc.publisher.institution | University of Cape Town | |
dc.source | Journal of Physics A: Mathematical and Theoretical | en_ZA |
dc.source.uri | http://iopscience.iop.org/journal/0305-4470 | |
dc.title | A numerical study of the large-period limit of a Zakharov-Shabat eigenvalue problem with periodic potentials | en_ZA |
dc.type | Journal Article | en_ZA |
uct.type.filetype | Text | |
uct.type.filetype | Image | |
uct.type.publication | Research | en_ZA |
uct.type.resource | Article | en_ZA |