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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 Harmonic resonance phenomena on nonlinear SH waves(Işık University Press, 2023-04) Ahmetolan, Semra; Özdemir, Neşe; Peker Dobie, Ayşe; Demirci, AliThe interaction of shear horizontal (SH) waves in a two layered elastic medium and its mth harmonic component is studied. The dispersion relation is analysed to obtain the wave number-phase velocity pairs where the third and fifth harmonic resonance phenomena emerge. By employing an asymptotic perturbation method it is shown that the balance between the weak nonlinearity and dispersion yields a coupled nonlinear Schrödinger (CNLS) equation for the slowly varying amplitudes of the fundamental wave and its fifth harmonic component. The nonlinearity effects of the materials and the ratio of layers’ thicknesses on the linear instabilities of solutions and the existence of solitary waves are examined.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 Contribution of higher order terms to the nonlinear shallow water waves(Işık University Press, 2012-05-12) Demiray, HilmiIn this work, by utilizing the scaled multiple-space expansion method, we studied the propagation of weakly nonlinear waves in shallow water 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 that of obtained by the modified reductive perturbation method [12]. We also proposed a method for the evolution equation governing the n th order term in the perturbation expansion. By defining a single time parameter we showed the connection of the modified reductive perturbation method to the scaled multiple-space expansion method.
