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A numerical study of the spectrum of the nonlinear Schrodinger equation
Thesis (MSc (Mathematical Sciences. Applied Mathematics))--Stellenbosch University, 2008.
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| Format: | Thesis |
| Language: | English |
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Stellenbosch : Stellenbosch University
2008
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| _version_ | 1867613933641138176 |
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| access_status_str | Open Access |
| author | Olivier, Carel Petrus |
| author2 | Herbst, B. M. |
| author_browse | Herbst, B. M. Olivier, Carel Petrus |
| author_facet | Herbst, B. M. Olivier, Carel Petrus |
| author_sort | Olivier, Carel Petrus |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc (Mathematical Sciences. Applied Mathematics))--Stellenbosch University, 2008. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/1744 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:44:01Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2008 |
| publishDateRange | 2008 |
| publishDateSort | 2008 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/1744 A numerical study of the spectrum of the nonlinear Schrodinger equation Olivier, Carel Petrus Herbst, B. M. Barashenkov, I. V. Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Applied Mathematics. Nonlinear Schrodinger equation Nonlinear spectrum Dissertations -- Applied mathematics Theses -- Applied mathematics Gross-Pitaevskii equations Thesis (MSc (Mathematical Sciences. Applied Mathematics))--Stellenbosch University, 2008. The NLS is a universal equation of the class of nonlinear integrable systems. The aim of this thesis is to study the NLS numerically. More speci cally, an algorithm is developed to calculate its nonlinear spectrum. The nonlinear spectrum is then used as a diagnostic for numerical studies of the NLS. The spectrum consists of a discrete part, further subdivided into the main part, the auxiliary part, and the continuous spectrum. Two algorithms are developed for calculating the main spectrum. One is based on Floquet theory, rst implemented by Overman [12]. The other is a direct calculation of the eigenvalues by Herbst and Weideman [16]. These algorithms are combined through the marching squares algorithm to calculate the continuous spectrum. All ideas are illustrated by numerical examples. 2008-11-24T13:45:57Z 2010-06-01T08:32:08Z 2008-11-24T13:45:57Z 2010-06-01T08:32:08Z 2008-12 Thesis http://hdl.handle.net/10019.1/1744 en Stellenbosch University application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Nonlinear Schrodinger equation Nonlinear spectrum Dissertations -- Applied mathematics Theses -- Applied mathematics Gross-Pitaevskii equations Olivier, Carel Petrus A numerical study of the spectrum of the nonlinear Schrodinger equation |
| title | A numerical study of the spectrum of the nonlinear Schrodinger equation |
| title_full | A numerical study of the spectrum of the nonlinear Schrodinger equation |
| title_fullStr | A numerical study of the spectrum of the nonlinear Schrodinger equation |
| title_full_unstemmed | A numerical study of the spectrum of the nonlinear Schrodinger equation |
| title_short | A numerical study of the spectrum of the nonlinear Schrodinger equation |
| title_sort | numerical study of the spectrum of the nonlinear schrodinger equation |
| topic | Nonlinear Schrodinger equation Nonlinear spectrum Dissertations -- Applied mathematics Theses -- Applied mathematics Gross-Pitaevskii equations |
| url | http://hdl.handle.net/10019.1/1744 |
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