الفهرس 
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Abstract
In this thesis a recent method viz tI Similarity method” described
by Sophus Lie, is used to find the solutions of some differential
equations frequently appear in describing natural phenomena
This method has the following advantages:-
Firstly: Reducing the number of independent variables in differential
equation by one .
Secondly: Finding the number of different solutions for the differential
equation.
Thirdly: Knowning a previous solution for differential equation, one
can construct another one.
The thesis consists of an introduction and four charpters
Their contents are as follows:
Chapter I :
In this chapter the author discussed the method under consideration
and its use in finding the solutions of partial differential equationsas
well as producing the groups of transformation.
Chapter II :
The author used the similarity method to find different solutions
in five cases for the one - dimensional Fokker Planck’s equation.
Chapter III :
This chapter includes two parts; in the first one the author used the
similarity method to find most of the probable solutions for the
fragmentation equation, whereas in the second part, the similarity
method is also used to find the different solutions for the
coagulation equation.
Chapter IV:
In this chapter the author used the similarity method to find
solutions for the two - dimensional Fokker-Planck equations.