17 sonuçlar
Arama Sonuçları
Listeleniyor 1 - 10 / 17
Yayın A note on the amplitude modulation of symmetric regularized long-wave equation with quartic nonlinearity(Springer, 2012-12) Demiray, HilmiWe study the amplitude modulation of a symmetric regularized long-wave equation with quartic nonlinearity through the use of the reductive perturbation method by introducing a new set of slow variables. The nonlinear Schrodinger (NLS) equation with seventh order nonlinearity is obtained as the evolution equation for the lowest order term in the perturbation expansion. It is also shown that the NLS equation with seventh order nonlinearity assumes an envelope type of solitary wave solution.Yayın Modulation of electron-acoustic waves in a plasma with vortex electron distribution(Walter De Gruyter GMBH, 2015-04) Demiray, HilmiIn the present work, employing a one-dimensional model of a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution and stationary ions, we study the amplitude modulation of electron-acoustic waves by use of the conventional reductive perturbation method. Employing the field equations with fractional power type of nonlinearity, we obtained the nonlinear Schrodinger equation as the evolution equation of the same order of nonlinearity. Seeking a harmonic wave solution with progressive wave amplitude to the evolution equation it is found that the NLS equation with fractional power assumes envelope type of solitary waves.Yayın A study of higher order terms in shallow water waves via modified PLK method(Walter De Gruyter GMBH, 2014-04) Demiray, HilmiIn this work, by utilizing the modified PLK (Poincare-Lighthill-Kou) method, we studied the propagation of weakly nonlinear waves in a shallow water theory and obtained the Korteweg-deVries (KdV) and the linearized KdV equations with non-homogeneous term as the governing equations of various order terms in the perturbation expansion. The result obtained here is exactly the same with that of Kodama and Taniuti [6], who employed the so-called "re-normalization method". 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 consistent with the results of Demiray [12], wherein the modified reductive perturbation method had been utilized.Yayın An application of the modified reductive perturbation method to a generalized boussinesq equation(Walter De Gruyter GMBH, 2013-02) Demiray, HilmiIn 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.Yayın Modulation of generalized symmetric regularized long-wave equation: generalized nonlinear Schrödinger equation(Freund Publishing House Ltd, 2010-12) Demiray, HilmiIn this work, the application of "the modified reductive perturbation method" is extended to the generalized symmetric regularized long-wave equation for strongly dispersive case and the contribution of higher order terms in the perturbation expansion is obtained. It is shown that the first order term in the perturbation expansion is governed by the generalized nonlinear Schrödinger quation whereas the second order term is governed by the generalized linear Schrödinger equation with a nonhomogeneous term. A travelling wave type of solution to these evolution equations is also given.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 Amplitude modulation of nonlinear waves in a fluid-filled tapered elastic tube(Wiley-V C H Verlag, 2003) Demiray, HilmiIn 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.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 Nonlinear wave modulation in a fluid-filled elastic tube with stenosis(Verlag Z Naturforsch, 2008-01) Demiray, HilmiIn the present work, treating the arteries as a thin-walled and prestressed elastic tube with a stenosis and the blood as a Newtonian fluid with negligible viscosity, we have studied the amplitude modulation of nonlinear waves in such a composite system by use of the reductive perturbation method. The a governing evolution equation was obtained as the variable coefficient nonlinear Schrodinger (NLS) equation. By setting the stenosis function equal to zero, we observed that this variable coefficient NLS equation reduces to the conventional NLS equation. After introducing a new dependent variable and a set of new independent coordinates, we reduced the evolution equation to the conventional NLS equation. By seeking a progressive wave type of solution to this evolution equation we observed, that the wave trajectories are not straight lines anymore; they are rather some curves in the (xi, tau) plane. It was further observed that the wave speeds for both enveloping and harmonic waves are variable, and the speed of the enveloping wave increases with increasing axial distance, whereas the speed of the harmonic wave decreases with increasing axial coordinates. The numerical calculations indicated that the speed of the harmonic wave decreases with increasing time parameter, but the sensitivity of wave speed to this parameter is quite weak.Yayın Particle dynamics in the KdV approximation(Elsevier Science BV, 2012-12) Borluk, Handan; Kalisch, HenrikThe KdV equation arises in the framework of the Boussinesq scaling as a model equation for waves at the surface of an inviscid fluid. Encoded in the KdV model are relations that may be used to reconstruct the velocity field in the fluid below a given surface wave. In this paper, velocity fields associated to exact solutions of the KdV equation are found, and particle trajectories are computed numerically. The solutions treated here comprise the solitary wave, periodic traveling waves, and the two-soliton solutions. For solitary waves and periodic traveling waves, approximate particle paths are found in closed form.
