الفهرس 
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Abstract
During the last four decades much attention has been paid to the nonlinear studies on the Yang-Mills equations.
The present thesis is mainly devoted to study the exact solutions for Yang-Mills equations by different way.
The thesis consists of a general introduction, four chapters and a list of [references which are briefly summarized as follows:
In the introduction the subject is defined and reviewed from the time of Yang and Mills up to the recent literature.
The importance of the problem in various domains of mathematical physics is reported.
In chapter 0:
The important mathematical preliminaries, the basic concepts and the formulations of Yang-Mills gauge field theories are given.
: In chapter I:
The main objective of this chapter is the studying of the instanton solutions for self-dual gauge fields. The boundary and asymptotic conditions under which one solves the self-dual equations are discussed. The self-dual and anti-self-dual connections which are the most important extrema or minima of the action as well as the instanton solutions for self-dual Yang-Mills equations are reviewed.
In chapter II:
This chapter is mainly concerned with the self-dual solutions for SU(2) and SU(3) gauge fields on Euclidean space.
An attempt is paid here to find new solutions for the Yang-Mills equations on SU(2), when p is a function of <|> on Euclidean space as well as when p being a complex analytic function. The solutions by Dipankar Ray are studied. Finally a set of solutions for self-dual SU(2) gauge fields on .Euclidean space when
(|) = <Kx1,x2),p = p(x3,X4).
are obtained.
2
Moreover the self-dual SU(3) Yang-Mills fields parametrized in a R-gauge are solved via a particular two-function ansatz whenpj are complex analytic function, i = 1,2,3.
tin chapter III :
We present a set of exact solutions for self-dual SU(3) Yang-Mills fields by reducing the Yang Mills theory to sine-Gordon and Liouville theories in two dimensions together with the implementation of Backlund transformations to generate new classes of exact solutions.
References:
The references used in preparing this thesis were organized according b the alphabetical order of the researchers.