Yazar "Demiray, Hilmi" seçeneğine göre listele

Listeleniyor 1 - 20 / 106
  • Küçük Resim
    Yayın
    Amplitude modulation of nonlinear waves in a fluid-filled tapered elastic tube
    (Elsevier Science Inc, 2004-07-15) Bakırtaş, İlkay; Demiray, Hilmi
    In the present work, treating the arteries as a tapered, thin walled, long and circularly conical prestressed elastic tube and using the reductive perturbation method, we have studied the amplitude modulation of nonlinear waves in such a fluid-filled elastic tube. By considering the blood as an incompressible inviscid fluid the evolution equation is obtained as the nonlinear Schrodinger equation with variable coefficients. It is shown that this type of equations admit a solitary wave type of solution with variable wave speed. It is observed that, the wave speed decreases with distance for tubes with descending radius while it increases for tubes with ascending radius.
  • Küçük Resim
    Yayın
    Amplitude modulation of nonlinear waves in a fluid-filled tapered elastic tube
    (Wiley-V C H Verlag, 2003) Demiray, Hilmi
    In the present work, treating the arteries as a tapered, thin walled, long, and circularly conical prestressed elastic tube and using the reductive perturbation method, we have studied the amplitude modulation of nonlinear waves in such a fluid-filled elastic tube. By considering the blood as an incompressible non-viscous fluid, the evolution equation is obtained as the nonlinear Schrodinger equation with variable coefficients. It is shown that this type of equations admit a solitary wave type of solution with a variable wave speed. It is observed that the wave speed increases with distance for narrowing tubes while it decreases for expanding tubes.
  • Küçük Resim
    Yayın
    Amplitude modulation of nonlinear waves in fluid-filled tapered tubes
    (Consultants Bureau, 2003-12) Bakırtaş, İlkay; Demiray, Hilmi
    We study the modulation of nonlinear waves in fluid-filled prestressed tapered tubes. For this, we obtain the nonlinear dynamical equations of motion of a prestressed tapered tube filled with an incompressible inviscid fluid. Assuming that the tapering angle is small and using the reductive perturbation method, we study the amplitude modulation of nonlinear waves and obtain the nonlinear Schrodinger equation with variable coefficients as the evolution equation. A traveling-wave type of solution of such a nonlinear equation with variable coefficients is obtained, and we observe that in contrast to the case of a constant tube radius, the speed of the wave is variable. Namely, the wave speed increases with distance for narrowing. tubes and decreases for expanding tubes.
  • Küçük Resim
    Yayın
    An analysis of higher order terms for ion-acoustic waves by use of the modified Poincar,-Lighthill-Kuo method
    (Springer India, 2015-10) Demiray, Hilmi
    In this work, by utilizing the modified Poincar,-Lighthill-Kuo (PLK) method, we studied the propagation of weakly nonlinear waves in a collisionless cold plasma and obtained the governing evolution equations of various order terms in the perturbation expansion. Seeking a progressive wave solution to these evolution equations we obtained the speed correction terms so as to remove some possible secularities. The result obtained here is exactly the same with those of the modified reductive perturbation and re-normalization methods. The method presented here is quite simple and based on introducing a new set of stretched coordinates.
  • Küçük Resim
    Yayın
    Analysis of periodic and solitary waves in a magnetosonic quantum dusty plasma
    (Springer, 2021-06) Demiray, Hilmi; Abdikian, Alireza
    The propagation of nonlinear magnetosonic waves in electron–ion–dust (complex) plasmas has been studied by considering the effects of Bohm potential in the presence of an external magnetic field. By using the quantum hydrodynamic model and applying the reductive perturbation method, the Kadomtsev–Petviashvili (KP) equation is obtained. The compressive structures of magnetosonic solitary waves and periodic travelling waves are studied. The effects of the electron to dust density ratio, the quantum plasma parameter, and the dust equilibrium density on the nonlinear magnetosonic periodic travelling waves are discussed. It is observed that the wave structure is more sensitive to the changes in the ratio of electron to dust densities, as compared to the changes in other physical parameters. The obtained results may be useful for a better understanding of obliquely nonlinear magnetosonic travelling waves of localized structures with a small amplitude in dense magnetized quantum dusty plasmas.
  • Küçük Resim
    Yayın
    Analytical approximate solutions for nonplanar Burgers equations by weighted residual method
    (Elsevier B.V., 2020-08-13) Demiray, Hilmi; El-Zahar, Essam Roshdy
    In this work, analytical approximate progressive wave solutions for the generalized form of the nonplanar KdV-Burgers (KdV-B) and mKdV-Burgers (mKdV-B) equations are presented and the results are discussed. Motivated with the exact solutions of the planar KdV-B and mKdV-B equations, the weighted residual method is applied to propose analytical approximate solutions for the generalized form of the nonplanar KdV-B and mKdV-B equations. The structure of the KdV-B equation assumes a solitary wave type of solution, whereas the mKdV-B equation assumes a shock wave type of solution. The analytical approximate progressive wave solutions for the cylindrical(spherical) KdV-B and mKdV-B equations are obtained as some special cases and compared with numerical solutions and the results are depicted on 2D and 3D figures. The results revealed that both solutions are in good agreement. The advantage of the present method is that it is rather simple as compared to the inverse scattering method and gives the same results with the perturbative inverse scattering technique. Moreover, the present analytical solutions allow readers to carry out physical parametric studies on the behavior of the solution. In addition to the present solutions are defined overall the problem domain not only over the grid points, as well as the solution calculation has less CPU time-consuming and round-off error.
  • Küçük Resim
    Yayın
    Analytical solution for nonplanar waves in a plasma with q-nonextensive nonthermal velocity distribution:Weighted residual method
    (Elsevier Ltd, 2020-01) Demiray, Hilmi
    The basic nonlinear equations describing the dynamics of a two component plasma consisting of cold positive ions and electrons obeying hybrid q- nonextensive nonthermal velocity distribution are examined in the cylindrical(spherical) coordinates through the use of reductive perturbation method and the cylindrical(spherical) KdV and the modified KdV equations are obtained. An approximate analytical method for the progressive wave solution is presented for these evolution equation in the sense of weighted residual method. It is observed that both amplitudes and the wave speeds decrease with the time parameter ?. Since the wave profiles change with ?, the waves cannot be treated as solitons. It is further observed that the amplitudes of spherical waves are larger than those of the cylindrical waves; and the wave amplitudes of modified KdV equation are much larger than those of the KdV equation. The effects of physical parameters (?, q) on the wave characteristics are also discussed.
  • Küçük Resim
    Yayın
    An analytical solution to the dissipative nonlinear Schrodinger equation
    (Elsevier Science, 2003-12-20) Demiray, Hilmi
    Motivated with a solitary wave type of solution to the nonlinear Schrodinger (NLS) equation, in this work we shall seek a travelling wave solution to the dissipative NLS equation by use of the hyperbolic tangent method. It is observed that the dissipative NLS equation still assumes a solitary wave type of solution with decaying amplitude in the time parameter.
  • 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.
  • Küçük Resim
    Yayın
    An application of modified reductive perturbation method to long water waves
    (Pergamon-Elsevier Science Ltd, 2011-12) Demiray, Hilmi
    In this work, we extended the application of "the modified reductive perturbation method" to long water waves and obtained the governing equations as the KdV hierarchy. Seeking a localized travelling wave solutions to these evolution equations we determined the scale parameter c(1) so as to remove the possible secularities that might occur. The present method is seen to be fairly simple as compared to the renormalization method [Kodama, Y., & Taniuti, T. (1977). Higher order approximation in reductive perturbation method 1. Weakly dispersive system. Journal of Physics Society of Japan, 45, 298-310] and the multiple scale expansion method [Kraenkel, R. A., Manna, M. A., & Pereira, J. G. (1995). The Korteweg-deVries hierarchy and long water waves. Journal of Mathematics Physics, 36, 307-320].
  • Küçük Resim
    Yayın
    An application of modified reductive perturbation method to symmetric regularized-long-wave
    (Işık University Press, 2011-03-24) Demiray, Hilmi
    In this work, we extended the application of "the modified reductive perturbation method" to symmetrical regularized long waves with quadratic nonlinearity and obtained various form of KdV equations as the governing equations. Seeking a localized travelling wave solutions to these evolution equations we determined the scale parameters g(1) and g(2) so as to remove the possible secularities that might occur. To indicate the power and elegance of the present method, we compared our result with the exact travelling wave solution of the symmetric regularized long-wave equation with quadratic nonlinearity. These results show that for weakly nonlinear case the solutions for both approaches coincide with each other. The present method is seen to be fairly simple as compared to the renormalization method of Kodama and Taniuti [4] and the multiple scale expansion method of Kraenkel et al [6].
  • Küçük Resim
    Yayın
    An application of multiple-time scale perturbation method to nonlinear ion-acoustic waves
    (Physical Soc Japan, 2012-02) Demiray, Hilmi
    In this work, by utilizing the multiple-time scale expansion method, we studied the propagation of weakly nonlinear waves in a collisionless cold plasma and obtained the governing evolution equations of various order terms in the perturbation expansion. Seeking a progressive wave solution to these evolution equations we obtained the speed correction terms so as to remove some possible secularities. By defining a single time parameter we showed the connection of the modified reductive perturbation method to the multiple-time scale expansion method.
  • Küçük Resim
    Yayın
    An application of the modified reductive perturbation method to a generalized boussinesq equation
    (Walter De Gruyter GMBH, 2013-02) Demiray, Hilmi
    In this work, we apply "the modified reductive perturbation method" to the generalized Boussinesq equation and obtain various form of generalized KdV equations as the evolution equations. Seeking a localized travelling wave solutions for these evolution equations we determine the scale parameters g(1) and g(2), which corresponds to the correction terms in the wave speed, so as to remove the possible secularities that might occur. Depending on the sign and the values of certain parameters the resulting solutions are shown to be a solitary wave or a periodic solution. The suitability of the method is also shown by comparing the results with the exact travelling wave solution for the generalized Boussinesq equation.
  • Küçük Resim
    Yayın
    An approximate wave solution for perturbed KDV and dissipative NLS equations: weighted residual method
    (Işık University Press, 2019-06-21) Demiray, Hilmi
    In the present work, we modified the conventional "weighted residual method" to some nonlinear evolution equations and tried to obtain the approximate progressive wave solutions for these evolution equations. For the illustration of the method we studied the approximate progressive wave solutions for the perturbed KdV and the dissipative NLS equations. The results obtained here are in complete agreement with the solutions of inverse scattering method. The present solutions are even valid when the dissipative effects are considerably large. The results obtained are encouraging and the method can be used to study the cylindrical and spherical evolution equations.
  • Küçük Resim
    Yayın
    The boundary layer approximation and nonlinear waves in elastic tubes
    (Pergamon-Elsevier Science, 2000-09) Antar, Nalan; Demiray, Hilmi
    In the present work, employing the nonlinear equations of an incompressible, isotropic and elastic thin tube and approximate equations of an incompressible viscous fluid, the propagation of weakly nonlinear waves is examined. In order to include the geometrical and structural dispersion into analysis, the wall's inertial and shear deformation are taken into account in determining the inner pressure-inner cross sectional area relation. Using the reductive perturbation technique, the propagation of weakly nonlinear waves, in the long-wave approximation, are shown to be governed by the Korteweg-de Vries (KdV) and the Korteweg-de Vries-Burgers (KdVB), depending on the balance between the nonlinearity, dispersion and/or dissipation. In the case of small viscosity (or large Reynolds number), the behaviour of viscous fluid is quite close to that ideal fluid and viscous effects are confined to a very thin layer near the boundary. In this case, using the boundary layer approximation we obtain the viscous-Korteweg-de Vries and viscous-Burgers equations.
  • Küçük Resim
    Yayın
    A complex travelling wave solution to the KdV-Burgers equation
    (Elsevier Science bv, 2005-09-19) Demiray, Hilmi
    In the present work, making use of the hyperbolic tangent method a complex travelling wave solution to the KdV-Burgers equation is obtained. It is observed that the real part of the solution is the combination of a shock and a solitary wave whereas the imaginary part is the product of a shock with a solitary wave. By imposing some restrictions on the field variable at infinity, two complex waves, i.e., right going and left going waves with specific wave speed are obtained.
  • Küçük Resim
    Yayın
    Complex travelling wave solutions to the KdV and Burgers equations
    (Elsevier Science Inc, 2005-03) Demiray, Hilmi
    In the present work, making use of the hyperbolic tangent method, some complex travelling wave solutions to the Korteweg-deVries and Burgers equations are obtained. It is observed that the real part of the Solution for the Burgers equation is of shock type whereas the imaginary part is the localized travelling wave. However, for the solution of the Korteweg-deVries equation the real part is a solitary wave while the imaginary part is the product of a solitary wave with a shock.
  • Küçük Resim
    Yayın
    Contribution of higher order terms in electron-acoustic solitary waves with vortex electron distribution
    (Springer Basel AG, 2014-12) Demiray, Hilmi
    The basic equations describing the nonlinear electron-acoustic waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions, in the long-wave limit, are re-examined through the use of the modified PLK method. Introducing the concept of strained coordinates and expanding the field variables into a power series of the smallness parameter epsilon, a set of evolution equations is obtained for various order terms in the perturbation expansion. The evolution equation for the lowest order term in the perturbation expansion is characterized by the conventional modified Korteweg-deVries (mKdV) equation, whereas the evolution equations for the higher order terms in the expansion are described by the degenerate(linearized) mKdV equation. By studying the localized traveling wave solution to the evolution equations, the strained coordinate for this order is determined so as to remove possible secularities that might occur in the solution. It is observed that the coefficient of the strained coordinate for this order corresponds to the correction term in the wave speed. The numerical results reveal that the contribution of second order term to the wave amplitude is about 20 %, which cannot be ignored.
  • Küçük Resim
    Yayın
    Contribution of higher order terms in nonlinear ion-acoustic waves: strongly dispersive case
    (Physical Soc Japan, 2002-08) Demiray, Hilmi
    Contribution of higher order terms in the perturbation expansion for the strongly dispersive ion-plasma waves is examined through the use of modified reductive perturbation method developed by us [J. Phys. Soc. Jpn. 68 (1999) 1833]. In the analysis it is shown that the lowest order term in the expansion is governed by the nonlinear Schrodinger equation while the second order term is governed by the linear Schrodinger equation. For the small wave number region a set of solution is presented for the evolution equations.
  • Küçük Resim
    Yayın
    Contribution of higher order terms to the nonlinear shallow water waves
    (Işık University Press, 2012-05-12) Demiray, Hilmi
    In this work, by utilizing the scaled multiple-space expansion method, we studied the propagation of weakly nonlinear waves in shallow water and obtained the governing evolution equations of various order terms in the perturbation expansion. Seeking a progressive wave solution to these evolution equations we obtained the speed correction terms so as to remove some possible secularities. The result obtained here is exactly the same with that of obtained by the modified reductive perturbation method [12]. We also proposed a method for the evolution equation governing the n th order term in the perturbation expansion. By defining a single time parameter we showed the connection of the modified reductive perturbation method to the scaled multiple-space expansion method.