This thesis is concerned with the anti-self-dual Yang-Mills equations and their reductions to Bogomol’nyi equations on constant curvature spaces. Chapters 1 and 2 contain introductory material. Chapter 1 discusses the origin of the equations in particle physics and their role in integrable systems. Chapter 2 describes the equations and the reduction process and outlines the construction of solutions via the twistor transform. In Chapter 3 we consider Bogomol’nyi equations on (2 + 1)-dimensional manifolds and show that for constant curvature space-times the equations are integrable and consider solutions in the negative scalar curvature case. In Chapter 4 we cover the negative scalar curvature case in more detail, constructing a number of soliton solutions including non-trivial scattering and consider the zero-curvature limit. In Chapter 5 we consider Bogomornyi equations in 3- diniensional hyperbolic space, derive an ansatz for solutions of the equation and use it to construct a number of new solutions. Chapter 6 contains concluding remarks.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:410946 |
| Date | January 2004 |
| Creators | Hickin, D. G. |
| Publisher | Durham University |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://etheses.dur.ac.uk/3037/ |
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