الفهرس 
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Abstract
The object of this thesis is to obtain explicit solutions for some of nonlinear
partial differential equations (NLPDE) using Darboux Transformation (DT). This
method starts from the partial differential equations Lax pair.
We performed in this thesis four tasks
1- The deduction of Lax pair for NLPDE equations.
2- The solution of integrable systems using Darboux transformation.
3- Derive one and two soliton solutions.
4- Test different seeds solutions.
The thesis contains five chapters described hereafter;
Chapter one
This chapter contains an introduction to several methods for solving non-linear
partial differential equations. These methods are divided into;
i- Analytical methods.
ii- Numerical methods.
In each section a review of each method is given.
Cbapter two
In this chapter we study the Darboux transformation method in details and
deduce the Lax pair equations for KdV and Hirota-Satsuma equations.
At the end of this chapter we apply our method to solve KdV and
Boussinesq equations.