I am currently working in the mathematics department, Zawia Univesity holding the position of lecturer. Research interests are Numerical Methods and Analytical Methods for Differential equations, and others.
In this paper, new optic solutions of (2+1)-dimensional generalization of complex nonlinear Schrö... more In this paper, new optic solutions of (2+1)-dimensional generalization of complex nonlinear Schrödinger equations are obtained via the powerful Extended Jacobian Elliptic functions expansion method. When the modulus 1 m or 0 m , the doubly periodic solutions degenerate soliton solutions including bright or dark solitons.
Journal of Advances in Mathematics and Computer Science
In this paper, the Laplace decomposition method (LDM) and some modification, namely the Modified ... more In this paper, the Laplace decomposition method (LDM) and some modification, namely the Modified Laplace decomposition method (MLDM), are adopted to numerically investigate the optic soliton solution of the nonlinear complex Schrödinger equation (NLSE). The obtained results demonstrate the reliability and the efficiency of the considered methods to numerically approximate such initial value problems (IVPs).
In this work, we aimed to construct a variety of solitary travelling wave solutions of a wide cla... more In this work, we aimed to construct a variety of solitary travelling wave solutions of a wide class of nonlinear partial differential equations (PDE's) that is governed by a presented single nonlinear partial differential equation (PDE) using the powerful modified extended Tanh method with Riccati equation. More general solutions are successfully constructed including the previous known formal solutions such as shock wave, periodic and weirstrass solutions.
An extended Tanh-function method with Riccati equation is presented for constructing multiple exa... more An extended Tanh-function method with Riccati equation is presented for constructing multiple exact travelling wave solutions of some nonlinear evolution equations which are particular cases of a generalized equation. The results of solitary waves are general compact forms with non-zero constants of integration. Taking the full advantage of the Riccati equation improves the applicability and reliability of the Tanh method with its extended form.
In this paper, the Adomian decomposition method (ADM) and the modified decomposition method (MDM)... more In this paper, the Adomian decomposition method (ADM) and the modified decomposition method (MDM) have been implemented for finding the solutions of Korteweg-de Vries and modified Korteweg-de Vries equations. The precision and speed of convergence of the numerical solution are verified through tables and illustrations via Mathematica software.
In this paper, we are using the extended sech function method along with a type of cole-Hopf tran... more In this paper, we are using the extended sech function method along with a type of cole-Hopf transformation to obtain the solutions for the nonlinear Korteweg-de Vries (KdV) equation. These types of solutions are represented as the hyperbolic function solutions including the solitary wave solution, shock wave solution and trigonometric function solution when the modulus m approaches to 1 and 0. Mathematica software is used in calculation and graphics.
In this paper, the main objective is to find the exact solitary travelling wave solution of the n... more In this paper, the main objective is to find the exact solitary travelling wave solution of the nonlinear modified Korteweg –de Vries (mKdV) equation using the improved Cole-Hopf transformation and the extend Sech function method. The presented methods have been successfully implemented for the equation of the interest.
In this paper, new optic solutions of (2+1)-dimensional generalization of complex nonlinear Schrö... more In this paper, new optic solutions of (2+1)-dimensional generalization of complex nonlinear Schrödinger equations are obtained via the powerful Extended Jacobian Elliptic functions expansion method. When the modulus m →1 or m →0 , the doubly periodic solutions degenerate soliton solutions including bright or dark solitons.
In this work, we aimed to construct a variety of solitary travelling wave solutions of a wide cla... more In this work, we aimed to construct a variety of solitary travelling wave solutions of a wide class of nonlinear partial differential equations (PDE's) that is governed by a presented single nonlinear partial differential equation (PDE) using the powerful modified extended Tanh method with Riccati equation. More general solutions are successfully constructed including the previous known formal solutions such as shock wave, periodic and weirstrass solutions.
In this paper, new optic solutions of (2+1)-dimensional generalization of complex nonlinear Schrö... more In this paper, new optic solutions of (2+1)-dimensional generalization of complex nonlinear Schrödinger equations are obtained via the powerful Extended Jacobian Elliptic functions expansion method. When the modulus 1 m or 0 m , the doubly periodic solutions degenerate soliton solutions including bright or dark solitons.
Journal of Advances in Mathematics and Computer Science
In this paper, the Laplace decomposition method (LDM) and some modification, namely the Modified ... more In this paper, the Laplace decomposition method (LDM) and some modification, namely the Modified Laplace decomposition method (MLDM), are adopted to numerically investigate the optic soliton solution of the nonlinear complex Schrödinger equation (NLSE). The obtained results demonstrate the reliability and the efficiency of the considered methods to numerically approximate such initial value problems (IVPs).
In this work, we aimed to construct a variety of solitary travelling wave solutions of a wide cla... more In this work, we aimed to construct a variety of solitary travelling wave solutions of a wide class of nonlinear partial differential equations (PDE's) that is governed by a presented single nonlinear partial differential equation (PDE) using the powerful modified extended Tanh method with Riccati equation. More general solutions are successfully constructed including the previous known formal solutions such as shock wave, periodic and weirstrass solutions.
An extended Tanh-function method with Riccati equation is presented for constructing multiple exa... more An extended Tanh-function method with Riccati equation is presented for constructing multiple exact travelling wave solutions of some nonlinear evolution equations which are particular cases of a generalized equation. The results of solitary waves are general compact forms with non-zero constants of integration. Taking the full advantage of the Riccati equation improves the applicability and reliability of the Tanh method with its extended form.
In this paper, the Adomian decomposition method (ADM) and the modified decomposition method (MDM)... more In this paper, the Adomian decomposition method (ADM) and the modified decomposition method (MDM) have been implemented for finding the solutions of Korteweg-de Vries and modified Korteweg-de Vries equations. The precision and speed of convergence of the numerical solution are verified through tables and illustrations via Mathematica software.
In this paper, we are using the extended sech function method along with a type of cole-Hopf tran... more In this paper, we are using the extended sech function method along with a type of cole-Hopf transformation to obtain the solutions for the nonlinear Korteweg-de Vries (KdV) equation. These types of solutions are represented as the hyperbolic function solutions including the solitary wave solution, shock wave solution and trigonometric function solution when the modulus m approaches to 1 and 0. Mathematica software is used in calculation and graphics.
In this paper, the main objective is to find the exact solitary travelling wave solution of the n... more In this paper, the main objective is to find the exact solitary travelling wave solution of the nonlinear modified Korteweg –de Vries (mKdV) equation using the improved Cole-Hopf transformation and the extend Sech function method. The presented methods have been successfully implemented for the equation of the interest.
In this paper, new optic solutions of (2+1)-dimensional generalization of complex nonlinear Schrö... more In this paper, new optic solutions of (2+1)-dimensional generalization of complex nonlinear Schrödinger equations are obtained via the powerful Extended Jacobian Elliptic functions expansion method. When the modulus m →1 or m →0 , the doubly periodic solutions degenerate soliton solutions including bright or dark solitons.
In this work, we aimed to construct a variety of solitary travelling wave solutions of a wide cla... more In this work, we aimed to construct a variety of solitary travelling wave solutions of a wide class of nonlinear partial differential equations (PDE's) that is governed by a presented single nonlinear partial differential equation (PDE) using the powerful modified extended Tanh method with Riccati equation. More general solutions are successfully constructed including the previous known formal solutions such as shock wave, periodic and weirstrass solutions.
Uploads