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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 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 Freezing optical rogue waves by Zeno dynamics(Elsevier Science BV, 2018-04-15) Bayındır, Cihan; Özaydın, FatihWe investigate the Zeno dynamics of the optical rogue waves. Considering their usage in modeling rogue wave dynamics, we analyze the Zeno dynamics of the Akhmediev breathers, Peregrine and Akhmediev-Peregrine soliton solutions of the nonlinear Schrodinger equation. We show that frequent measurements of the wave inhibits its movement in the observation domain for each of these solutions. We analyze the spectra of the rogue waves under Zeno dynamics. We also analyze the effect of observation frequency on the rogue wave profile and on the probability of lingering of the wave in the observation domain. Our results can find potential applications in optics including nonlinear phenomena.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.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, CihanIn 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.
