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2009 - 200912010 - 20183
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Scopus Q: Q1 × Konu: Control nonlinearities ×

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Listeleniyor 1 - 4 / 4
  • Küçük Resim
    Yayın
    Variable coefficient modified KdV equation in fluid-filled elastic tubes with stenosis: Solitary waves
    (Pergamon-Elsevier Science Ltd, 2009-10-15) Demiray, Hilmi
    In the present work, treating the arteries as a thin walled prestressed elastic tube with variable radius, and using the longwave approximation, we have studied the propagation of weakly nonlinear waves in such a fluid-filled elastic tube, by employing the reductive perturbation method. By considering the blood as an incompressible non-viscous fluid, the evolution equation is obtained as variable coefficients Korteweg-de Vries equation. Noticing that for a set of initial deformations, the coefficient characterizing the nonlinearity vanish, by re-scaling the stretched coordinates we obtained the variable coefficient modified KdV equation. Progressive wave solution is sought for this evolution equation and it is found that the speed of the wave is variable along the tube axis.
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    Cylindrical and spherical solitary waves in an electron-acoustic plasma with vortex electron distribution
    (Amer Inst Physics, 2018-04) Demiray, Hilmi; El-Zahar, Essam Roshdy
    We consider the nonlinear propagation of electron-acoustic waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions. The basic nonlinear equations of the above described plasma are re-examined in the cylindrical (spherical) coordinates by employing the reductive perturbation technique. The modified cylindrical (spherical) KdV equation with fractional power nonlinearity is obtained as the evolution equation. Due to the nature of nonlinearity, this evolution equation cannot be reduced to the conventional KdV equation. A new family of closed form analytical approximate solution to the evolution equation and a comparison with numerical solution are presented and the results are depicted in some 2D and 3D figures. The results reveal that both solutions are in good agreement and the method can be used to obtain a new progressive wave solution for such evolution equations. Moreover, the resulting closed form analytical solution allows us to carry out a parametric study to investigate the effect of the physical parameters on the solution behavior of the modified cylindrical (spherical) KdV equation.
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    Modulation of cylindrical (spherical) waves in a plasma with vortex electron distribution
    (American Institute of Physics Inc., 2018-07-01) Demiray, Hilmi
    In the present work, employing cylindrically (spherically) symmetric field equations of a plasma consisting of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution and stationary ions, we studied the amplitude modulation of electron-acoustic waves. Due to the physical nature of the problem under investigation, the nonlinearity of the field equations is of order (3/2), which causes considerable difficulty in the analysis of modulation problems. To solve this difficulty, we expanded this nonlinear term into the Fourier cosine series of the phase function and obtained the modified cylindrical (spherical) nonlinear Schrodinger (NLS) equation. A consistent analysis for the modulational instability is presented and a criterion between the time parameter tau and the wave number K is established. In addition, motivated with the solitonic solution of modified NLS equation for planar case and utilizing the "weighted residual method," we proposed a harmonic wave of variable frequency with progressive wave amplitude to the evolution equation. It is found that the modified cylindrical (spherical) NLS equation assumes an envelope type of progressive wave solution in the sense weighted residual. The numerical results reveal that the amplitude of spherical wave is much larger than that of the cylindrical wave and that both amplitudes decrease with increasing time parameter tau. It is further observed that the wave profiles get distorted with progressing time.
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    Yayın
    A note on the cylindrical solitary waves in an electron-acoustic plasma with vortex electron distribution
    (Amer Inst Physics, 2015-09) Demiray, Hilmi; Bayındır, Cihan
    In the present work, we consider the propagation of nonlinear electron-acoustic non-planar waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions. The basic nonlinear equations of the above described plasma are re-examined in the cylindrical coordinates through the use reductive perturbation method in the long-wave approximation. The modified cylindrical Korteweg-de Vries equation with fractional power nonlinearity is obtained as the evolution equation. Due to the nature of nonlinearity, which is fractional, this evolution equation cannot be reduced to the conventional Korteweg-de Vries equation. An analytical solution to the evolution equation, by use of the method developed by Demiray [Appl. Math. Comput. 132, 643 (2002); Comput. Math. Appl. 60, 1747 (2010)] and a numerical solution by employing a spectral scheme are presented and the results are depicted in a figure. The numerical results reveal that both solutions are in good agreement.