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1. Extended method of quasilinearization for a three-point boundary value problem with general nonlinear nonconvex boundary conditions (Co-author: Ahmed Alsaedi)
International Journal of Mathematics, Game Theory and Algebra, 15(1), 13-19 (2005).
Abstract: In this paper, we apply the generalized quasilinearization technique to obtain a monotone sequence of approximate solution converging monotonically and quadratically to the unique solution of a second order three-point boundary value problem with general nonlinear nonconvex boundary condition.
2. Solitary wave solutions for the nonlinear Ito system, KAAU Journal, Science (accepted) .
Abstract: In this paper, we look for some new solitary wave solutions for the nonlinear Ito coupled system. For this purpose, we improved the extended tanh method to construct more new exact doubly-periodic solutions in terms of tanh and Jacobi elliptic functions of nonlinear Ito system.The solitary wave solutions and triangular periodic solutions also can be obtained .
3. Limitation of Adomian and Homotopy method, International Journal of Pure and Apllied Mathematics, 46(2), 251-260 (2008)
Abstract: It is usual to resort to Adomian decomposition method or to homotopy analysis method for the solution of nonlinear problem. We show by considering a simple example that, in the absence of an asymptotic analysis, these methods fail to provide any significant information beyond a finite interval
4 . Jacobic elliptic functions and New Algebraic Method for the systems of Partial Differential Equations, Indian Journal of Mathematics and Mathematical Sciences.
Abstract: A new algebraic method is devised to obtain a series of exact solutions and more general solutions to a system of Drinfeld- Sokolov-Wilson and New exact solution for a system of nonlinear Euler equations are obtained by using Jacobin elliptic functions
based on the idea of the homogeneous balance method.
5. Relativistic Electron Beam Instability in an Inhomogeneous Cold Plasma (Co Auther: Kh. H. El-Shorbagy) International Mathematical Forum (IMF).
Abstract: The interaction of relativistic electron beam (REB) with an inhomogenous cold plasma on the spatial growing of beam-plasma instability has been studied. The variation in the plasma density does have a profound effect on the spatial beam-plasma instability. Besides, relativistic effect leads to more power absorption from the relativistic electron beam so REB causing a resonant increase of the electric field. This work may have its interest due its link to HF heating of plasmas.
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