Aly R. Seadawy

Bio: Aly R. Seadawy is an academic researcher from Taibah University. The author has contributed to research in topics: Nonlinear system & Soliton. The author has an hindex of 62, co-authored 360 publications receiving 9884 citations. Previous affiliations of Aly R. Seadawy include COMSATS Institute of Information Technology & Beni-Suef University.

Stability analysis for Zakharov-Kuznetsov equation of weakly nonlinear ion-acoustic waves in a plasma

Abstract: The Zakharov-Kuznetsov (ZK) equation is an isotropic nonlinear evolution equation, first derived for weakly nonlinear ion-acoustic waves in a strongly magnetized lossless plasma in two dimensions. In the present study, by applying the extended direct algebraic method, we found the electric field potential, electric field and magnetic field in the form of traveling wave solutions for the two-dimensional ZK equation. The solutions for the ZK equation are obtained precisely and the efficiency of the method can be demonstrated. The stability of these solutions and the movement role of the waves are analyzed by making graphs of the exact solutions.

Stability analysis solutions for nonlinear three-dimensional modified Korteweg–de Vries–Zakharov–Kuznetsov equation in a magnetized electron–positron plasma

Abstract: The nonlinear three-dimensional modified Korteweg–de Vries–Zakharov–Kuznetsov ​(mKdV–ZK) equation governs the behavior of weakly nonlinear ion-acoustic waves in magnetized electron–positron plasma which consists of equal hot and cool components of each species. By using the reductive perturbation procedure leads to a mKdV–ZK equation governing the oblique propagation of nonlinear electrostatic modes. The stability of solitary traveling wave solutions of the mKdV–ZK equation to three-dimensional long-wavelength perturbations is investigated. We found the electrostatic field potential and electric field in form traveling wave solutions for three-dimensional mKdV–ZK equation. The solutions for the mKdV–ZK equation are obtained precisely and efficiency of the method can be demonstrated.

Approximation solutions of derivative nonlinear Schrödinger equation with computational applications by variational method

Abstract: The derivative nonlinear Schrodinger (DNLS) equation is a nonlinear dispersive model that appears in the description of wave propagation in a plasma. The existence of a Lagrangian and the invariant variational principle for two coupled equations are given. The two coupled equations is describing the nonlinear evolution of the Alfven wave with magnetosonic waves at much larger scale. A type of the coupled DNLS equations is studied by means of symbolic computation, which can describe the wave propagation in birefringent optical fibers. The functional integral corresponding to those equations is derived. We investigate the approximation solutions of the DNLS equation by choice of a trial function in the region of the rectangular box in two cases. By using this trial functions, the functional integral and the Lagrangian of the system without loss are found. The general case for the two-box potential can be obtained on the basis of a different ansatz, where we approximate the Jost function by series in the tanh function method instead of the piece-wise linear function.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Applied Mathematics and Computation

Abstract: The work is giving estimations of the discrepancy between solutions of the initial and the homogenized problems for a one{dimensional second order elliptic operators with random coeecients satisfying strong or uniform mixing conditions. We obtain several sharp estimates in terms of the corresponding mixing coeecient. Abstract. In the theory of homogenisation it is of particular interest to determine the classes of problems which are stable on taking the homogenisation limits. A notable situation where the limit enlarges the class of original problems is known as memory (nonlocal) eeects. A number of results in that direction has been obtained for linear problems. Tartar (1990) innitiated the study of the eeective equation corresponding to nonlinear equation: @ t u n + a n u 2 n = f: Signiicant progress has been hampered by the complexity of required computations needed in order to obtain the terms in power{series expansion. We propose a method which overcomes that diiculty by introducing graphs representing the domain of integration of the integrals in each term. The graphs are relatively simple, it is easy to calculate with them and they give us a clear image of the form of each term. The method allows us to discuss the form of the eeective equation and the convergence of power{series expansions. The feasibility of our method for other types of nonlinearities will be discussed as well.

Waves in Dusty Space Plasmas

Abstract: Preface. 1. Plasmas and Dust. 2. Charging Mechanisms and Experiments. 3. Space Observations. 4. Multispecies Formalism and Waves. 5. Electrostatic Modes. 6. Electromagnetic Modes. 7. Fluctuating Dust Charges. 8. Self-Gravitation. 9. Mass and Size Distributions. 10. Other Modes. 11. Conclusions and Outlook. Bibliography. Index.