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Asymptotic analysis of the parametrically driven damped nonlinear evolution equation
Bibliography: pages 179-184.
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2016
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| _version_ | 1867613332691746816 |
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| access_status_str | Open Access |
| author | Duba, Chuene Thama |
| author_browse | Duba, Chuene Thama |
| author_facet | Duba, Chuene Thama |
| author_sort | Duba, Chuene Thama |
| collection | Thesis |
| description | Bibliography: pages 179-184. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/22076 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:34:27.383Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/22076 Asymptotic analysis of the parametrically driven damped nonlinear evolution equation Duba, Chuene Thama Applied Mathematics Bibliography: pages 179-184. Singular perturbation methods are used to obtain amplitude equations for the parametrically driven damped linear and nonlinear oscillator, the linear and nonlinear Klein-Gordon equations in the small-amplitude limit in various frequency regimes. In the case of the parametrically driven linear oscillator, we apply the Lindstedt-Poincare method and the multiple-scales technique to obtain the amplitude equation for the driving frequencies Wdr ~ 2ω₀,ω₀, (2/3)ω₀ and (1/2)ω₀. The Lindstedt-Poincare method is modified to cater for solutions with slowly varying amplitudes; its predictions coincide with those obtained by the multiple-scales technique. The scaling exponent for the damping coefficient and the correct time scale for the parametric resonance are obtained. We further employ the multiple-scales technique to derive the amplitude equation for the parametrically driven pendulum for the driving frequencies Wdr ~ 2ω₀, ω₀, (2/3)ω₀, (1/2)ω₀ and 4ω₀. We obtain the correct scaling exponent for the amplitude of the solution in each of these frequency regimes. 2016-10-03T13:56:52Z 2016-10-03T13:56:52Z 1997 Master Thesis Masters MSc http://hdl.handle.net/11427/22076 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Applied Mathematics Duba, Chuene Thama Asymptotic analysis of the parametrically driven damped nonlinear evolution equation |
| thesis_degree_str | Master's |
| title | Asymptotic analysis of the parametrically driven damped nonlinear evolution equation |
| title_full | Asymptotic analysis of the parametrically driven damped nonlinear evolution equation |
| title_fullStr | Asymptotic analysis of the parametrically driven damped nonlinear evolution equation |
| title_full_unstemmed | Asymptotic analysis of the parametrically driven damped nonlinear evolution equation |
| title_short | Asymptotic analysis of the parametrically driven damped nonlinear evolution equation |
| title_sort | asymptotic analysis of the parametrically driven damped nonlinear evolution equation |
| topic | Applied Mathematics |
| url | http://hdl.handle.net/11427/22076 |
| work_keys_str_mv | AT dubachuenethama asymptoticanalysisoftheparametricallydrivendampednonlinearevolutionequation |