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## The preliminary group classification of the equation utt = f(x,ux)uxx + g(x, ux)

We study the class of partial differential equations Utt = f(x, ux)uxx +

g(x, u x), with arbitrary functions f(x, u x) and g(x, u x), from the point of view

of group classification. The principal Lie algebra of infinitesimal symmetries

admitted by the whole class is three-dimensional. We use the method of preliminary

group classification to obtain a classification of these equations with

respect to a one-dimesional extension of the principal Lie algebra and then a

countable-dimensional subalgebra of their equivalence algebra. Each of these

equations admits an additional infinitesimal symmetry. L.V. Ovsiannikov [9]

has proposed an algorithm to construct efficiently the optimal system of an

arbitrary decomposable Lie algebra. We use this algorithm to construct an

optimal system of subalgebras of all dimensionalities (from one-dimensional

to six- dimensional) of a seven-dimensional solvable Lie algebra. / Thesis (M.Sc)-University of Durban-Westville, 1995.

Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:ukzn/oai:http://researchspace.ukzn.ac.za:10413/5139 |

Date | January 1995 |

Creators | Narain, Ojen Kumar. |

Contributors | Kambule, M. T. |

Source Sets | South African National ETD Portal |

Language | English |

Detected Language | English |

Type | Thesis |

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