الفهرس 
chapter 1Only 14 pages are availabe for public view
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Abstract
Nonlinear evolution equations (NLEEs) anse in many physical problems like, fluid mechanics, plasma physics, condensed matter physics and optics, <xhibiting a rich variety of nonlinear phenomena. The analytical and umerical solutions of NLEEs are actually one of the central research themes as those equations have many physical applications. Such problems are solved using numerical methods and analytical one such as the inverse scattering transformation (1ST), Darboux and Backlund transformations, Hirota’s bilinear method, Lie symmetry transformation. It is to be noticed that most of the previous researches since two decades until now are related to the reduction of the original non linear partial differential equation, while the reduction of its Lax pair is much less frequent.We do in this thesis present an analytical solution of two non linear evolution problems; a generalized Hirota-Satsuma equation III three dimensions and (2+ 1) Boiti-Leon-Manna-Pempinelli equation. As Lax pairs consist in a simplification of the original non linear partial
differential equations. We started with them. For each problem this pair was reduced to a system of ordinary differential equations using a two parameter group method. By a homogenous balance of the reduced Lax system, new <solutions were derived. The two problems considered here, were published
[199,200].
This work consists of five chapters as follows