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Konu: Solitary waves × WoS Q: Q3 ×

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    Interactions of nonlinear waves in fluid-filled elastic tubes
    (Verlag Z Naturforsch, 2007-02) Demiray, Hilmi
    In 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.
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    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.
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    A modified reductive perturbation method as applied to nonlinear ion-acoustic waves
    (Physical Society Japan, 1999-06) Demiray, Hilmi
    The 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.
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    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.
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    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.
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    Modulation of electron-acoustic waves in a plasma with kappa distribution
    (American Institute of Physics Inc., 2016-03) Demiray, Hilmi
    In 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.
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    The modified reductive perturbation method as applied to the Boussinesq equation
    (Verlag Z Naturforsch, 2007-08) Demiray, Hilmi
    In this work, we extended the application of "the modified reductive perturbation method" to long water waves and obtained the governing equations of Korteweg-de Vries (KdV) hierarchy. Seeking localized travelling wave solutions to these evolution equations we have determined the scale parameter g, so as to remove the possible secularities that might occur. To indicate the effectiveness and the elegance of the present method, we studied the problem of the "dressed solitary wave method" and obtained exactly the same result. The present method seems to be fairly simple and practical as compared to the renormalization method and the multiple scale expansion method existing in the current literature.