د. الفيتوري محمد عمر2025-03-052025-03-05https://dspace.academy.edu.ly/handle/123456789/1388This thesis deals with problems arising in the study of nonlinear partial differential equations (PDEs) in mathematical physics. Three methods namely, the generalized G G        -expansion method, the new mapping method and the new Jacobi elliptic function expansion method have applied for finding the exact wave solutions of the nonlinear PDEs. Families of exact solutions including Jacobi elliptic functions solutions, hyperbolic (kink and anti-kink solitons, bell (bright) and anti-bell (dark) solitary wave solutions), trigonometric (periodic solutions) and rational solutions . This thesis contains three chapters. In chapter one, we apply the generalized G G        -expansion method to find the exact traveling wave solutions of the nonlinear PDE describing the nonlinear low-pass electrical lines and the nonlinear PDE describing pulse narrowing nonlinear transmission lines. With the aid of computer algebra systems (CAS) such as Maple or Mathematical and Jacobi elliptic equation G2  R QG2 PG4 many new Jacobi elliptic functions solutions are constructed, where R, Q and P are constants . In chapter two, we apply the new mapping method combined with the first order nonlinear ordinary differential equation (ODE) 2 2 4 6 1 1 ( ) p ( ) ( ) ( ) r, 2 3 F   F   qF   sF   p, q, s and r are constants  to find the exact traveling wave solutions of the higher-order nonlinear Schrödinger equation (NLS) with derivative non-kerr nonlinear terms and the higher -order dispersive nonlinear Schrödinger equation. In chapter three, we apply the new Jacobi elliptic function expansion method to find the solitons and other exact wave solutions of some nonlinear PDEs namely, the nonlinear PDE governing wave propagation in nonlinear low-passe electrical transmission lines, the nonlinear modified KdV (mKdV) equation and the nonlinear Benjamin-Bona-Mahoney (BBM) equationThis thesis deals with problems arising in the study of nonlinear partial differential equations (PDEs) in mathematical physics. Three methods namely, the generalized G G        -expansion method, the new mapping method and the new Jacobi elliptic function expansion method have applied for finding the exact wave solutions of the nonlinear PDEs. Families of exact solutions including Jacobi elliptic functions solutions, hyperbolic (kink and anti-kink solitons, bell (bright) and anti-bell (dark) solitary wave solutions), trigonometric (periodic solutions) and rational solutions . This thesis contains three chapters. In chapter one, we apply the generalized G G        -expansion method to find the exact traveling wave solutions of the nonlinear PDE describing the nonlinear low-pass electrical lines and the nonlinear PDE describing pulse narrowing nonlinear transmission lines. With the aid of computer algebra systems (CAS) such as Maple or Mathematical and Jacobi elliptic equation G2  R QG2 PG4 many new Jacobi elliptic functions solutions are constructed, where R, Q and P are constants . In chapter two, we apply the new mapping method combined with the first order nonlinear ordinary differential equation (ODE) 2 2 4 6 1 1 ( ) p ( ) ( ) ( ) r, 2 3 F   F   qF   sF   p, q, s and r are constants  to find the exact traveling wave solutions of the higher-order nonlinear Schrödinger equation (NLS) with derivative non-kerr nonlinear terms and the higher -order dispersive nonlinear Schrödinger equation. In chapter three, we apply the new Jacobi elliptic function expansion method to find the solitons and other exact wave solutions of some nonlinear PDEs namely, the nonlinear PDE governing wave propagation in nonlinear low-passe electrical transmission lines, the nonlinear modified KdV (mKdV) equation and the nonlinear Benjamin-Bona-Mahoney (BBM) equationSolitons Solutions and Other Solutions for Some Nonlinear Partial Differential Equations in Mathematical Physics