dc.contributor.advisor | Khalique, C.M. | en_US |
dc.contributor.advisor | Motsepa, T. | en_US |
dc.contributor.author | Adeyemo, O.D. | en_US |
dc.date.accessioned | 2020-08-03T10:37:01Z | |
dc.date.available | 2020-08-03T10:37:01Z | |
dc.date.issued | 2019 | en_US |
dc.identifier.uri | https://orcid.org/0000-0002-8745-5387 | en_US |
dc.identifier.uri | http://hdl.handle.net/10394/35448 | |
dc.description | MSc (Applied Mathematics), North-West University, Mafikeng Campus | |
dc.description.abstract | In this work we examine two nonlinear partial differential equations of fluid mechan-ics. The modified equal-width (MEW) equation, which is used in handling the sim-ulation of a single dimensional wave propagation in nonlinear media with dispersion process, is studied first. We compute the optimal system of one-dimensional subalge-bras and then use it to perform symmetry reductions and obtain group-invariant solutions. Also, we derive conservation laws of the MEW equation using the multiplier approach and the Noether theorem. Secondly we study the generalized nonlinear advection-diffusion equation, which describes the movement of a buoyancy-driven plume in an inclined porous medium. We consider three cases of n and in each case, we construct optimal system of one-dimensional subalgebras using the computed Lie point symmetries and then obtain symmetry reductions and group-invariant solutions based on these optimal systems of one-dimensional subalgebra. In addition, we de-termine the conservation laws of the equation by employing the multiplier approach and the new conservation theorem due to Ibragimov. | en_US |
dc.language.iso | en | en_US |
dc.publisher | North-West University (South Africa) | en_US |
dc.title | Symmetry analysis of modified equal-width and nonlinear advection-diffusion equations | en_US |
dc.type | Thesis | en_US |
dc.description.thesistype | Masters | en_US |
dc.contributor.researchID | 20559860 - Khalique, Chaudry Masood (Supervisor) | en_US |
dc.contributor.researchID | 24602825 - Motsepa, Tanki (Supervisor) | en_US |