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Yayın Interactions of nonlinear waves in fluid-filled elastic tubes(Verlag Z Naturforsch, 2007-02) Demiray, HilmiIn this work, treating an artery as a prestressed thin-walled elastic tube and the blood as an inviscid fluid, the interactions of two nonlinear waves propagating in opposite directions are studied in the longwave approximation by use of the extended PLK (Poincare-Lighthill-Kuo) perturbation method. The results show that up to O(k(3)), where k is the wave number, the head-on collision of two solitary waves is elastic and the solitary waves preserve their original properties after the interaction. The leading-order analytical phase shifts and the trajectories of two solitons after the collision are derived explicitly.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, HilmiIn 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.Yayın A modified reductive perturbation method as applied to nonlinear ion-acoustic waves(Physical Society Japan, 1999-06) Demiray, HilmiThe basic equations describing the nonlinear ion-acoustic waves in a cold collisionless plasma, in the longwave limit, is re-examined through the use of a modified reductive perturbation method. Introducing the concept of a scale parameter and expanding the variables and the scale parameter into a power series of the smallness parameter epsilon, a set of evolution equations is obtained for various order terms in the perturbation expansion. To illustrate the present derivation, a localized travelling wave solution is studied for the derived field equations and the result is compared with those of obtained by Sugimoto and Kakutani(3)) who introduced some slow scales, Kodama and Taniuti(4)) who employed the renormalization method and Malfliet and Wieers,(6)) who employed the dressed solitary wave approach from the outset of their study.Yayın A complex travelling wave solution to the KdV-Burgers equation(Elsevier Science bv, 2005-09-19) Demiray, HilmiIn 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.Yayın Cylindrical and spherical solitary waves in an electron-acoustic plasma with vortex electron distribution(Amer Inst Physics, 2018-04) Demiray, Hilmi; El-Zahar, Essam RoshdyWe 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.Yayın Modulation of cylindrical (spherical) waves in a plasma with vortex electron distribution(American Institute of Physics Inc., 2018-07-01) Demiray, HilmiIn 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.Yayın Amplitude modulation of nonlinear waves in fluid-filled tapered tubes(Consultants Bureau, 2003-12) Bakırtaş, İlkay; Demiray, HilmiWe 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.Yayın Contribution of higher order terms in nonlinear ion-acoustic waves: strongly dispersive case(Physical Soc Japan, 2002-08) Demiray, HilmiContribution 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.Yayın Modulation of electron-acoustic waves in a plasma with kappa distribution(American Institute of Physics Inc., 2016-03) Demiray, HilmiIn the present work, employing a one dimensional model of an unmagnetized collisionless plasma consisting of a cold electron fluid, hot electrons obeying ? velocity distribution, and stationary ions, we study the amplitude modulation of an electron-acoustic waves by use of the conventional reductive perturbation method. Employing the field equations of such a plasma, we obtained the nonlinear Schrödinger equation as the evolution equation. Seeking a harmonic wave solution with progressive wave amplitude to the evolution equation, as opposed to the plasma with vortex distribution, the amplitude wave assumes a shock wave type of solution. Finally, the modulational stability of the wave is studied and it is observed that the wave is modulationally stable for all admissible wave numbers.Yayın Interactions of nonlinear electron-acoustic solitary waves with vortex electron distribution(American Institute of Physics Inc., 2015-02-01) Demiray, HilmiIn the present work, based on a one dimensional model, we consider the head-on-collision of nonlinear electron-acoustic waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions. The analysis is based on the use of extended Poincare, Lighthill-Kuo method [C. H. Su and R. M. Mirie, J. Fluid Mech. 98, 509 (1980); R. M. Mirie and C. H. Su, J. Fluid Mech. 115, 475 (1982)]. It is shown that, for the first order approximation, the waves propagating in opposite directions are characterized by modified Korteweg-de Vries equations. In contrary to the results of previous investigations on this subject, we showed that the phase shifts are functions of both amplitudes of the colliding waves. The numerical results indicate that the waves with larger amplitude experience smaller phase shifts. Such a result seems to be plausible from physical considerations.
