الفهرس 
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Abstract
The exact solutions, Lie point symmetries and conservation laws of nonlinear partial differential equations (NLPDEs) have become recently one of the most essential task in many nonlinear models for understanding some physical phenomena for it. Also, Lie symmetry method considered a powerful tool for finding many solutions and conservation laws for these models. There are many methods that have been used to construct solitary wave solutions and conservation
laws of NLPDEs such the extended F-expansion method, the multiplier method, the Ibragimov’s theorem, the Kudryashov method, Lie symmetry method and
other methods.
The aim of this study:
The aim of this study is investigation of some solutions and conservation laws for different types of NLPDEs and systems that have important applications in physical sciences. Also clarify the properties of some solutions that we will get
via geometrical shape.
Study plain:
This thesis consists of six chapters, in each chapter, we studied some important physical models by different methods as follows:
• By using the extended Kudryashov method, we studied Schamel-nonlinear Schrödinger (S-NLS) equation, Schamel Korteweg-de Vries (S-KdV) equation, Schamel Korteweg-de Vries Burgers (S-KdVB) and Schamel equation.
• We applied the extended F-expansion method, the Lie symmetry method and Ibragimov’s theorem for ion sound and Langmuir waves equations (ISLWs).
• We studied classical Boussinesq (CB) system by applying the Lie symmetry method, Ibragimov’s theorem and the generalized tanh-function method.
• We studied the Calogero-Bogoyavlenskii-Schiff (CBS) equation with
variable coefficients by applying the Lie symmetry method, Ibragimov’s theorem and the modified F-expansion method.
• We studied the Bernoulli sub-equation function method, the Lie symmetry method and the multiplier method of two important physical models, the hyperbolic nonlinear Schrödinger (HNLS) equation and the Heisenberg ferromagnetic spin chain (HFSC) equation.
The results:
• We can be constructed explicit exact solutions of S-NLS equation, S-KdV equation, S-KdVB and Schamel equation.
• We obtained novel exact solutions of ISLWs, also, we constructed the conservation laws.
• We investigated new travelling wave solutions for the CB system. Also, we obtained the adjoint table, the commutator table, the group transformations of Lie algebra and the conservation laws for this system.
• We obtained various exact solutions for CBS equation with variable coefficients. Also, we obtained the adjoint table, the commutator table and the conservation laws for this system.
• We constructed new exact solutions for the HNLS equation and the HFSC equation. Also, we obtained the conservation laws and the group transformations and by these group transformations, we obtained novel exact solutions for these equations.
Recommendations:
• We will apply the Lie symmetry method to fractional differential equations to construct many new types of exact solutions and conservation laws.
• We will use the conservation laws to study some properties of the solution such as the stability, the existence, the uniqueness and the integrability of PDEs.