An analysis of the symmetries and conservation laws of some classes of nonlinear wave equations in curved spacetime geometry
Autor: | Jamal, S |
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Jazyk: | angličtina |
Rok vydání: | 2013 |
Předmět: | |
Druh dokumentu: | Diplomová práce |
Popis: | A thesis submitted to the Faculty of Science, University of the Witwatersrand, in requirement for the degree Doctor of Philosophy, Johannesburg, 2013. The (1+3) dimensional wave and Klein-Gordon equations are constructed using the covariant d'Alembertian operator on several spacetimes of interest. Equations on curved geometry inherit the nonlinearities of the geometry. These equations display interesting properties in a number of ways. In particular, the number of symmetries and therefore, the conservation laws reduce depending on how curved the manifold is. We study the symmetry properties and conservation laws of wave equations on Freidmann-Robertson-Walker, Milne, Bianchi, and de Sitter universes. Symmetry structures are used to reduce the number of unknown functions, and hence contribute to nding exact solutions of the equations. As expected, properties of reduction procedures using symmetries, variational structures and conservation laws are more involved than on the well known at (Minkowski) manifold. |
Databáze: | Networked Digital Library of Theses & Dissertations |
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