3. Electronic Theses and Dissertations (ETDs) - All submissions

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Author: search.filters.author.Mathebula, AgreementSubject: search.filters.subject.Geometry

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    Symmetry classifications on a curved geometry
    (2020) Mathebula, Agreement
    In this thesis, we consider one-parameter point transformations that leave a differential equation invariant. In particular, we show that Noether symmetry classifications of any diagonal metric may be simplified by geometric criteria. We describe the Klein-Gordon equation for some general spaces and deal with the corresponding Killing algebra. Moreover, our investigation consists of several metrics, their Lie algebras, the point generators of the Klein-Gordon equation and their associated potential functions. Finally, we study a class of ecological diffusive equations and determine higher-order symmetries of non-linear diffusion equations
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