One of the more recently established methods of analysis of di erentials involves the
invariance properties of the equations and the relationship of this with the underlying
conservation laws which may be physical. In a variational system, conservation laws
are constructed using a well known formula via Noether's theorem. This has been
extended to non variational systems too. This association between symmetries and
conservation laws has initiated the double reduction of di erential equations, both
ordinary and, more recently, partial. We apply these techniques to a number of well
known equations like the damped driven Schr odinger equation and a transformed
PT symmetric equation(with Schr odinger like properties), that arise in a number
of physical phenomena with a special emphasis on Schr odinger type equations and
equations that arise in Optics.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/14771 |
| Date | 12 June 2014 |
| Creators | Masemola, Phetogo |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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