F. M . Ahmed | Zawia university (original) (raw)

Papers by F. M . Ahmed

Research paper thumbnail of New Optics Solutions for the Nonlinear (2+1)-Dimensional Generalization of Complex Nonlinear Schrödinger Equation

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.

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Research paper thumbnail of The Extended Sech Function Method and The Cole-Hopf Transformation for Solving the Nonlinear Korteweg-de Vries Equation

International Journal of Science and Research (IJSR), 2016

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Research paper thumbnail of Numerical Optics Soliton Solution of the Nonlinear Schrödinger Equation Using the Laplace and the Modified Laplace Decomposition Method

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).

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Research paper thumbnail of The Solitary Travelling Wave Solutions of Some Nonlinear Partial Differential Equations Using the Modified Extended Tanh Function Method with Riccati Equation

Asian Research Journal of Mathematics

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.

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Research paper thumbnail of Multiple Exact Travelling Solitary Wave Solutions of Nonlinear Evolution Equations

Asian Research Journal of Mathematics

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.

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Research paper thumbnail of Numerical Solutions of Some Nonlinear Partial Differential Equations by the Decomposition Method

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.

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Research paper thumbnail of The Extended Sech Function Method and The Cole- Hopf Transformation for Solving the Nonlinear Korteweg-de Vries Equation

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.

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Research paper thumbnail of Solitary Wave Solution of the Nonlinear Modified Korteweg-de Vries Equation Using the Improved Cole-Hopf Transformation and the Extended Sech function Method

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.

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Research paper thumbnail of New Optics Solutions for the Nonlinear (2+1)- Dimensional Generalization of Complex Nonlinear Schrödinger Equation

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.

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Research paper thumbnail of The Solitary Travelling Wave Solutions of Some Nonlinear Partial Differential Equations Using the Modified Extended Tanh Function Method with Riccati Equation

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.

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Research paper thumbnail of New Optics Solutions for the Nonlinear (2+1)-Dimensional Generalization of Complex Nonlinear Schrödinger Equation

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.

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Research paper thumbnail of The Extended Sech Function Method and The Cole-Hopf Transformation for Solving the Nonlinear Korteweg-de Vries Equation

International Journal of Science and Research (IJSR), 2016

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Research paper thumbnail of Numerical Optics Soliton Solution of the Nonlinear Schrödinger Equation Using the Laplace and the Modified Laplace Decomposition Method

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).

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Research paper thumbnail of The Solitary Travelling Wave Solutions of Some Nonlinear Partial Differential Equations Using the Modified Extended Tanh Function Method with Riccati Equation

Asian Research Journal of Mathematics

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.

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Research paper thumbnail of Multiple Exact Travelling Solitary Wave Solutions of Nonlinear Evolution Equations

Asian Research Journal of Mathematics

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.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Numerical Solutions of Some Nonlinear Partial Differential Equations by the Decomposition Method

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.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of The Extended Sech Function Method and The Cole- Hopf Transformation for Solving the Nonlinear Korteweg-de Vries Equation

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.

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Research paper thumbnail of Solitary Wave Solution of the Nonlinear Modified Korteweg-de Vries Equation Using the Improved Cole-Hopf Transformation and the Extended Sech function Method

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.

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Research paper thumbnail of New Optics Solutions for the Nonlinear (2+1)- Dimensional Generalization of Complex Nonlinear Schrödinger Equation

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.

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Research paper thumbnail of The Solitary Travelling Wave Solutions of Some Nonlinear Partial Differential Equations Using the Modified Extended Tanh Function Method with Riccati Equation

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.

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