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2019 - 20202
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Yazar: El-Zahar, Essam Roshdy × Konu: Analytical approximate solutions ×

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  • Küçük Resim
    Yayın
    On progressive wave solution for non-planar KDV equation in a plasma with q-nonextensive electrons and two oppositely charged ions
    (Işık University Press, 2020) Demiray, Hilmi; El-Zahar, Essam Roshdy; Shan, Shaukat Ali
    In this paper, the ion-acoustic wave is investigated in a plasma with q-nonextensive electrons and two oppositely charged ions with varying masses. These parameters are found to modify the linear dispersion relation and nonlinear solitary structures. The reductive perturbation method is employed to derive modified Korteweg-de Vries (KdV) equation. To solve the obtained governing evolution equation, the exact solution in the planar geometry is obtained and used to obtain an analytical approximate progressive wave solution for the nonplanar evolution equation. The analytical approximate solution so obtained is compared with the numerical solution of the same nonplanar evolution equation and the results are presented in 2D and 3D figures. The results revealed that both solutions are in good agreement. A parametric study is carried out to investigate the effect of different physical parameters on the nonlinear evolution solution behavior. The obtained solution allows us to study the impact of various plasma parameters on the behavior of the nonplanar ion-acoustic solitons. The suitable application of the present investigations can be found in laboratory plasmas, where oppositely charged ions and nonthermal electrons dwell.
  • Küçük Resim
    Yayın
    Analytical solutions of cylindrical and spherical dust ion-acoustic solitary waves
    (Elsevier B.V., 2019-06) El-Zahar, Essam Roshdy; Demiray, Hilmi
    In the present work, employing the conventional reductive perturbation method to the field equations of an unmagnetized dusty plasma consisting of inertial ions, Boltzmann electrons and stationary dust particles in the nonplanar geometry we derived cylindrical(spherical) KdV and mKdV equations. Being aware of the fact that there exists no exact analytical solution for the progressive waves for such evolution equations we presented the exact analytical solution of a generalized form of such evolution equations in the planar geometry and used this solution to obtain an analytical approximate progressive wave solution to the generalized evolution equation. Then the progressive wave solutions for the cylindrical(spherical) KdV and m-KdV equations is obtained as some special cases. The analytical approximate solutions so obtained are compared with the numerical solutions of these equations. The results reveal that both solutions are in a good agreement. One advantage of present analytical approximate solution is that it allows readers to gain information, share understandings, or carry out a physical parametric study on the evolution solution behavior as well as the solution calculation has no CPU time-consuming or round off error.