الفهرس 
EXACT SOLUTIONS FOR THE VARIABLEOnly 14 pages are availabe for public view
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Abstract
The purpose of this thesis is studying the Painlevé analysis and the symmetry
method to various nonlinear partial di¤erential equations to get exact solutions for
them: This thesis is divided into four chapters.
In Chapter (I): We con.ned our attention to the survey and development of the
di¤erent techniques that have been utilized in chapters II-VI to obtain exact solutions
of nonlinear partial di¤erential equations of physical and engineering interests:
In Chapter (II): The cubic nonlinear Klein-Gordon equation and the general-
ized Kuramoto-Sivashinsky equation have been analyzed via Painlevé analysis: Firstly,
we have carried out Painlevé analysis to cubic nonlinear Klein-Gordon equation then,
we have shown that the integrability condition is not satis.ed for arbitrary func-
tion _(x; t): Therefore, cubic nonlinear Klein-Gordon equation fails the Painlevé test:
Using Bäcklund and Kruskal.s transformations, we have obtained exact solutions:
Furthermore, the application of the Painlevé analysis to the generalized Kuramoto-
Sivashinsky equation has led to non-integer roots for the resonance involved in the
method: Therefore, the generalized Kuramoto-Sivashinsky equation fails the Painlevé
test: Using Bäcklund and Kruskal.s transformations, we have obtained new exact
solutions:
In Chapter (III): We con.ned our attention to solve the variable coe¢ cients
generalized Klein-Gordon equation and we have obtained new exact solutions when
we applied Painlevé analysis since we have found that this equation fails the Painlevé
test: Using Painlevé expansion and solving the integrability condition, we have ob-
tained new exact solutions:
ii
In Chapter (IV): The Quasi-linear wave equation has been analyzed via the
symmetry method: We have carried out the symmetry method for some cases for the
Quasi-linear wave equation and, we have got di¤erent group theoretic reductions for
these cases: Some of these reductions have led to exact solutions:
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