This research studies two nonlinear problems arising in mathematical physics. Firstly
the Korteweg-de Vrics-Burgers equation is considered. Lie symmetry method is
used to obtain t he exact solutions of Korteweg-de Vries-Burgers equation. Also
conservation laws are obtained for this equation using the new conservation theorem.
Secondly, we consider the generalized (2+ 1)-dimensional Zakharov-Kuznctsov (ZK)
equation of time dependent variable coefficients from the Lie group-theoretic point
of view. We classify the Lie point symmetry generators to obtain the optimal system
of one-dimensional subalgebras of t he Lie symmetry algebras. These subalgebras arc
then used to construct a number of symmetry reductions and exact group-invariant
solutions of the ZK equation. We utilize the new conservation theorem to construct
the conservation laws of t he ZK equation. / Thesis (M. Sci in Applied Mathematics) North-West University, Mafikeng Campus, 2011
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:nwu/oai:dspace.nwu.ac.za:10394/14404 |
| Date | January 2011 |
| Creators | Moleleki, Letlhogonolo Daddy |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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