Asymptotic analysis of the parametrically driven damped nonlinear evolution equation

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dc.contributor.authorDuba, Chuene Thamaen_ZA
dc.date.accessioned2016-10-03T13:56:52Z
dc.date.available2016-10-03T13:56:52Z
dc.date.issued1997en_ZA
dc.descriptionBibliography: pages 179-184.en_ZA
dc.description.abstractSingular 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.en_ZA
dc.identifier.apacitationDuba, C. T. (1997). <i>Asymptotic analysis of the parametrically driven damped nonlinear evolution equation</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/22076en_ZA
dc.identifier.chicagocitationDuba, Chuene Thama. <i>"Asymptotic analysis of the parametrically driven damped nonlinear evolution equation."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1997. http://hdl.handle.net/11427/22076en_ZA
dc.identifier.citationDuba, C. 1997. Asymptotic analysis of the parametrically driven damped nonlinear evolution equation. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Duba, Chuene Thama AB - 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. DA - 1997 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1997 T1 - Asymptotic analysis of the parametrically driven damped nonlinear evolution equation TI - Asymptotic analysis of the parametrically driven damped nonlinear evolution equation UR - http://hdl.handle.net/11427/22076 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/22076
dc.identifier.vancouvercitationDuba CT. Asymptotic analysis of the parametrically driven damped nonlinear evolution equation. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1997 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/22076en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherApplied Mathematicsen_ZA
dc.titleAsymptotic analysis of the parametrically driven damped nonlinear evolution equationen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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