الفهرس 
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Abstract
The aim of this thesis is applying some of a new methods to find the exact and solitary wave solutions for some models which in different fields of science like physics, mechanics, chemistry, biology,...etc. to provide with the explicit formulas of solutions which may give the physical information of each models and help to understand the mechanism of related physical models. In this thesis, we study some problems which play an important role in mathematical physics and biology. These problems have a nonlinear partial differential equations form. Many methods have employed for the analytic treatment of nonlinear partial differential equations. This thesis contains six chapters. In chapter 1: We give a historical overview for partial differential equations and several methods which are used to solve NPDEs. In chapter 2: We use the modified simple equation method to find the exact traveling wave solutions and solitary wave solutions for: The foam drainage equation, the (2+1)-dimensional breaking soliton equations and the (3+1)-dimensional KP equation n. chapter 3: We use extended tanh-function method to find the exact traveling wave solutions and solitary wave solutions for: The modified Liouville equation and the symmetric regularized long-wave equation In chapter 4: We use the (G’/G)-expansion method to find the exact traveling wave solutions and solitary wave solutions for: Modified Liouville equation and the generalized HirotaSatsuma couple KdV system. In chapter 5: We use extended Jacobian elliptic function expansion method to find the exact traveling wave solutions and solitary wave solutions for: Dynamical system in a new double-chain model of DNA, a diffusive predator-prey system and the couple BoitiLeon-Pempinelli system. In chapter 6: We use the exp(-ϕ(ξ))-expansion method to find the exact traveling wave solutions and solitary wave solutions for: The nonlinear Burger equation with power law nonlinearity, the perturbed nonlinear Schrodinger equation with Kerr law non linearity, Fitzhugh-Nagumo (FN) equation and the system of shallow water wave equations.