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26 results on '"El-Shewy, Emad K."'

4. Ion-Acoustic Waves in Unmagnitized Collisionless Weakly Relativistic Plasma using Time-Fractional KdV Equation

Author

El-Wakil, El-Said A., Abulwafa, Essam M., El-shewy, Emad K., and Mahmoud, Abeer A.

Subjects
Physics - Plasma Physics, Nonlinear Sciences - Pattern Formation and Solitons
Abstract

The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electrostatic ion-acoustic waves in unmagnitized collisionless weakly relativistic warm plasma. The Lagrangian of the time fractional KdV equation is used in similar form to the Lagrangian of the regular KdV equation. The variation of the functional of this Lagrangian leads to the Euler-Lagrange equation that leads to the time fractional KdV equation. The Riemann-Liouvulle definition of the fractional derivative is used to describe the time fractional operator in the fractional KdV equation. The variational-iteration method given by He is used to solve the derived time fractional KdV equation. The calculations of the solution with initial condition A0*sech(cx)^2 are carried out. The result of the present investigation may be applicable to some plasma environments, such as ionosphere., Comment: 16 pages+5 figures

Published
2010

5. Time-Fractional KdV Equation Describing the Propagation of Electron-Acoustic Waves in plasma

Author

El-Wakil, Elsaid A., Abulwafa, Essam M., El-shewy, Emad K., and Mahmoud, Abeer A.

Subjects
Physics - Plasma Physics, Nonlinear Sciences - Pattern Formation and Solitons
Abstract

The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electron-acoustic waves. The Lagrangian of the time fractional KdV equation is used in similar form to the Lagrangian of the regular KdV equation. The variation of the functional of this Lagrangian leads to the Euler-Lagrange equation that leads to the time fractional KdV equation. The Riemann-Liouvulle definition of the fractional derivative is used to describe the time fractional operator in the fractional KdV equation. The variational-iteration method given by He is used to solve the derived time fractional KdV equation. The calculations of the solution with initial condition A0*sech(cx)^2 are carried out. The result of the present investigation may be applicable to some plasma environments, such as the Earth's magnetotail region., Comment: about 17 pages + 6 figures

Published
2010

6. Solution of Time-Fractional Korteweg-de Vries Equation in warm Plasma

Author

El-Wakil, El-Said A., Abulwafa, Essam M., El-shewy, Emad K., and Mahmoud, Abeer A.

Subjects
Physics - Plasma Physics, Nonlinear Sciences - Pattern Formation and Solitons
Abstract

The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude ion-acoustic waves. The Lagrangian of the time fractional KdV equation is used in similar form to the Lagrangian of the regular KdV equation. The variation of the functional of this Lagrangian leads to the Euler-Lagrange equation that leads to the time fractional KdV equation. The Riemann-Liouvulle definition of the fractional derivative is used to describe the time fractional operator in the fractional KdV equation. The variational-iteration method given by He is used to solve the derived time fractional KdV equation. The calculations of the solution with initial condition A0*sech(cx)^2 are carried out. The result of the present investigation may be applicable to some plasma environments, such as ionosphere., Comment: The paper is in tex format+3 figures in eps

Published
2010

9. Numerical Investigation of the Fractional Diffusion Wave Equation with the Mittag–Leffler Function.

Author

Shafiq, Madiha, Abbas, Muhammad, El-Shewy, Emad K., Abdelrahman, Mahmoud A. E., Abdo, Noura F., and El-Rahman, Ali A.

Subjects
HEAT equation, FINITE differences, COMPUTER graphics, SPLINES, COMPUTER-aided design
Abstract

A spline is a sufficiently smooth piecewise curve. B-spline functions are powerful tools for obtaining computational outcomes. They have also been utilized in computer graphics and computer-aided design due to their flexibility, smoothness and accuracy. In this paper, a numerical procedure dependent on the cubic B-spline (CuBS) for the time fractional diffusion wave equation (TFDWE) is proposed. The standard finite difference (FD) approach is utilized to discretize the Atangana–Baleanu fractional derivative (ABFD), while the derivatives in space are approximated through the CuBS with a θ -weighted technique. The stability of the propounded algorithm is analyzed and proved to be unconditionally stable. The convergence analysis is also studied, and it is of the order O (h 2 + (Δ t) 2) . Numerical solutions attained by the CuBS scheme support the theoretical solutions. The B-spline technique gives us better results as compared to other numerical techniques. [ABSTRACT FROM AUTHOR]

Published
2024
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12. Effects of Brownian noise strength on new chiral solitary structures.

Author

Alharbi, Yousef F, El-Shewy, Emad K, and Abdelrahman, Mahmoud AE

Subjects
*BROWNIAN noise, *NONLINEAR Schrodinger equation, *APPLIED sciences, *NONLINEAR equations, *WIENER processes, *SOLITONS
Abstract

In this paper, we investigate the nonlinear Chiral Schrödinger equation (CNLSE) in two dimensions where noise term affected randomly with time. This equation characterized some edges states of fractional-Hall Effect features in quantum. The CNLSE with multiplicative noise effects is studied as dynamical system to specify the acceptable solution types and then solved by unified solver method. The presented solutions are periodic envelopes, explosive, dissipative, symmetric solitons, and blow up waves. It was confirmed that the noise factor is dominant on all the wave conversion, growing and damping of envelopes and shocks. The presented technique in this study can be easily utilized for other nonlinear equations in applied science. Mathematics Subject Classification (2010) : 35C08, 65C20, 60H15, 35Q40, 35Q55, 35Q62 [ABSTRACT FROM AUTHOR]

Published
2023
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13. The noise sense effects on the characteristic nonlinearly Schrödinger equation solitary propagations.

Author

Abdelwahed, Hesham G, El-Shewy, Emad K, Abdelrahman, Mahmoud A E, and Alghanim, Salim S

Subjects
*NOISE control, *BROWNIAN motion, *NOISE, *NONLINEAR waves, *SOLITONS, *SENSES, *SYMBOLIC computation
Abstract

The nonlinearly stochastic Schrödinger equation (NLSSE) predicts the nonlinear process that produces the waves decay in many physics applications. The unified method has been used in obtaining different new stochastic forms for NLSSE damped by noises in Itô sense. The derived structures appear in the form of rational, solitons, soliton-like shocks, and explosive propagations. The new stochastic solutions investigated the change of frequencies by noise term in NLSSE in nonlinear process that may be produced in many nonlinear wave applications. Finally, wave picture properties may controlled by noise term in Itô sense effect, which gives new information's for NLSSE in physics applications which is believed to be affected by the influence of Brownian motion that change the shape and structures of the generated decaying and damping waves. [ABSTRACT FROM AUTHOR]

Published
2023
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