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Yayın Asymptotic solutions of love wave propagation in a covered half-space with inhomogeneous initial stresses G(3)(1)(Işık University Press, 2015) Hasanoğlu, Elman; Negin, MasoudThe dispersive behavior of Love waves in an elastic half-space substrate covered by an elastic layer under the effect of inhomogeneous initial stresses has been investigated. Classical linearized theory of elastic waves in initially stressed bodies for small deformations is used and the well-known WKB high-frequency asymptotic technique is applied for the theoretical derivations. Numerical results on the action of the influence of the initial stresses on the wave propagation velocity for a geophysical example are presented and discussed.Yayın Head-on collision of the solitary waves in fluid-filled elastic tubes(Işık University Press, 2018-04-12) Özden, Ali Erinç; Demiray, HilmiIn the present work, by employing the field equations given in [15] and the extended PLK method derived in [9], we have studied the head-on collision of solitary waves in arteries. Introducing a set of stretched coordinates which include some unknown functions characterizing the higher order dispersive effects and the trajectory functions to be determined from the removal of possible secularities that might occur in the solution. Expanding these unknown functions and the field variables into power series of the smallness parameter epsilon and introducing the resulting expansions into the field equations we obtained the sets of partial differential equations. By solving these differential equations and imposing the requirements for the removal of possible secularities we obtained the speed correction terms and the trajectory functions. The results of our calculation show that both the evolution equations and the phase shifts resulting from the head-on collision of solitary waves are quite different from those of Xue [15], who employed the incorrect formulation of Su and Mirie [4]. As opposed to the result of previous works on the same subject, in the present work the phase shifts depend on the amplitudes of both colliding waves.Yayın An approximate wave solution for perturbed KDV and dissipative NLS equations: weighted residual method(Işık University Press, 2019-06-21) Demiray, HilmiIn 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.Yayın On progressive wave solution for non-planar KDV equation in a plasma with q-nonextensive electrons and two oppositely charged ions(Işık University Press, 2020) Demiray, Hilmi; El-Zahar, Essam Roshdy; Shan, Shaukat AliIn this paper, the ion-acoustic wave is investigated in a plasma with q-nonextensive electrons and two oppositely charged ions with varying masses. These parameters are found to modify the linear dispersion relation and nonlinear solitary structures. The reductive perturbation method is employed to derive modified Korteweg-de Vries (KdV) equation. To solve the obtained governing evolution equation, the exact solution in the planar geometry is obtained and used to obtain an analytical approximate progressive wave solution for the nonplanar evolution equation. The analytical approximate solution so obtained is compared with the numerical solution of the same nonplanar evolution equation and the results are presented in 2D and 3D figures. The results revealed that both solutions are in good agreement. A parametric study is carried out to investigate the effect of different physical parameters on the nonlinear evolution solution behavior. The obtained solution allows us to study the impact of various plasma parameters on the behavior of the nonplanar ion-acoustic solitons. The suitable application of the present investigations can be found in laboratory plasmas, where oppositely charged ions and nonthermal electrons dwell.Yayın Yayın Rotational Weingarten surfaces in hyperbolic 3-space(Birkhauser, 2020-04-01) Dursun, UğurWe study rotational Weingarten surfaces in the hyperbolic space H3(- 1) with the principal curvatures κ and λ satisfying a certain functional relation κ= F(λ) for a given continuous function F. We determine profile curves of such surfaces parameterized in terms of the principal curvature λ. Then we consider some special cases by taking F(λ) = aλ+ b and F(λ) = aλm for particular values of the constants a, b, and m.Yayın Tulczyjew's triplet for Lie groups III: higher order dynamics and reductions for iterated bundles(Serbian Society of Mechanics, 2021) Esen, Oğul; Gümral, Hasan; Sütlü, SerkanGiven a Lie group G, we elaborate the dynamics on T*T*G and T*TG, which is given by a Hamiltonian, as well as the dynamics on the Tul-czyjew symplectic space TT * G, which may be defined by a Lagrangian or a Hamiltonian function. As the trivializations we adapted respect the group structures of the iterated bundles, we exploit all possible subgroup reductions (Poisson, symplectic or both) of higher order dynamics.Yayın Modulational instability of three dimensional waves in a plasma with vortex electron distribution(Işık University Press, 2019-02-10) Demiray, HilmiIn the present work, employing the three dimensional equations 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 an electron-acoustic waves by use of the conventional reductive perturbation method. Employing the field equations with fractional power type of nonlinearity, we obtained the three dimensional form of the modified nonlinear Schrodinger equation as the evolution equation of the same order of nonlinearity. The modulational instability of the homogeneous harmonic solution is investigated and the criteria for the instability is discussed as a function of the obliqueness angle. The numerical calculations show that the critical value of the wave number of the envelop wave increases with the wave number k of the carrier wave and the obliqueness angle gamma.Yayın A note on the cylindrical waves with transverse distortion in a plasma with vortex electron distribution(Işık University Press, 2020-01-20) Demiray, HilmiIn the present work, employing the conventional reductive perturbation method and the nonlinear field equations of a plasma consisting of a cold electron uid, hot electrons obeying a non-isothermal (trapped/vortex-like) distribution and station-ary ions with transverse distortion, we studied the propagation of nonlinear waves in such a plasma medium and obtained the modified CKP equation. Seeking a progressive wave solution to this evolution equation we obtained the exact analytical solution. It is observed that the speed of the solitary wave is directional dependent and the wave front is not circularly cylindrical surface any more.Yayın Harmonic mappings related to starlike function of complex order ?(Işık University Press, 2014) Aydoğan, Seher MelikeLet SH be the class of harmonic mappings defined by SH = { f = h(z) + g(z) | h(z) = z + ?? n=2 anz?, g(z) = ?? n=1 bnz?} The purpose of this talk is to present some results about harmonic mappings which was introduced by R. M. Robinson [8].
