An analysis of the symmetries and conservation laws of some classes of nonlinear wave equations in curved spacetime geometry

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dc.contributor.author Jamal, S
dc.date.accessioned 2013-08-08T11:11:56Z
dc.date.available 2013-08-08T11:11:56Z
dc.date.issued 2013-08-08
dc.identifier.uri http://hdl.handle.net/10539/13028
dc.description A thesis submitted to the Faculty of Science, University of the Witwatersrand, in requirement for the degree Doctor of Philosophy, Johannesburg, 2013. en_ZA
dc.description.abstract 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. en_ZA
dc.language.iso en en_ZA
dc.subject.lcsh Geometry.
dc.subject.lcsh Symmetry (Mathematics)
dc.subject.lcsh Conservation laws (Mathematics)
dc.subject.lcsh Nonlinear waves.
dc.subject.lcsh Wave equation.
dc.title An analysis of the symmetries and conservation laws of some classes of nonlinear wave equations in curved spacetime geometry en_ZA
dc.type Thesis en_ZA


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