Abstract
M.Sc.
In this work we concentrate on two generalizations of Lie symmetries namely conditional
symmetries in the form of Q-symmetries and approximate symmetries. The theorems and
definitions presented can be used to obtain exact and approximate solutions for nonlinear
partial differential equations. These are then applied to various nonlinear heat and wave
equations and many interesting solutions are given.
Chapters 1 and 2 gives an introduction to the classical Lie approach.
Chapters 3, 4 and 5 deals with conditional -, approximate -, and approximate conditional
symmetries respectively.
In chapter 6 we give a review of symbolic algebra computer packages available to aid
in the search for symmetries, as well as useful REDUCE programs which were written
to obtain the results given in chapters 2 to 5.