Equivalence and symmetry groups of a nonlinear equation in plasma physics
Date
2016-07-14
Authors
Bashe, Mantombi Beryl
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Abstract
In this work we give a brief overview of the existing group classification methods
of partial differential equations by means of examples. On top of these methods
we introduce another new method which classify according to low-dimensional Lie
elgebras, One can ask: What is the aim of introducing a new method whilst there
are existing methods? This question is answered in the following paragraph.
Firstly we classify our system of non-linear partial differential equations using the
preliminary group classification method (one of the existing methods). The results
are not different from what; Euler, Steeb and Mulsor have obtained in 1991 and 1992.
That is, this method does not yield new information.
This new method which classifies according to low-dimensional Lie algebras is used
to classify a general system of equations from plasma physics. Finally, using this
method we completely classify our system for four-dimensionnl algebras. For a partial
differential equation to be completely classified using this method, it must admit a
low-dimensional Lie algebra.
Description
Degree awarded with distinction on 6 December 1995.
A research report submitted to the Faculty of Science, University of the
Witwatersrand, in fulfilment of the requirements for the degree of Masters.
Johannesburg, 1995.