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Yayın A note on the exact travelling wave solution to the KdV-Burgers equation(Elsevier Science, 2003-10) Demiray, HilmiIn the present note, by use of the hyperbolic tangent method, a progressive wave solution to the Korteweg-de Vries-Burgers (KdVB) equation is presented. The solution we introduced here is less restrictive and comprises some solutions existing in the current literature (see [Wave Motion 11 (1989) 559; Wave Motion 14 (1991) 369]).Yayın 3-D Vibration analysis of microstretch plates(Springer, 2008) İnan, Esin; Kiriş, AhmetIn the present work, rectangular plates with various boundary conditions are Studied, which are modeled by the rnicrostretch theory. Wave propagation problem is investigated and new waves are observed which do not appear in the classical theory of elasticity. Ritz method is used for this investigation. Triplicate Chebyshev series, multiplied by boundary functions, are used as admissible functions and the frequency equations of the micro-stretch plate are obtained by the use of Chebyshev-Ritz method. The additional frequencies due to the microstructure of the plate are observed among the values of the frequencies obtained from the classical theory of elasticity. We observed that these additional frequencies disappear while the all microstretch constants are taken as zero.Yayın On complex solutions of the eikonal equation(IEEE, 2007) Hasanoğlu, ElmanIn this paper a new approach of complex rays in an inhomogeneous medium is presented. Complex rays are complex solutions of the eikonal equation, the main equation of the geometical optics. It is shown that solving the eikonal equation by using the characteristic method naturally leads to the pseudoriemann and Minkowski geometries. In framework of these geometries complex rays , like the real ones, can be drawn in real space and they may have caustics, and caustics also can be drawn in real space.Yayın On the realization of optical mappings and transformation of amplitudes by means of an aspherical "thick" lens(Gustav Fischer Verlag, 2000) Hasanoğlu, Elman; Polat, Burak DenizThe constraints for the realization of a given optical mapping by means of an aspherical ''thick" lens are investigated by using the laws of geometrical optics. The analysis yields us a partial differential equation which the optical mapping functions must satisfy as a necessary and sufficient condition. It is shown that thick lenses, which convert plane waves to plane waves, can be considered as a pure amplitude element, An interesting feature of this equation is that it does not involve the lens profiles. The problem of realization is later discussed for some special mappings and graphical illustrations of the aspherical lens profiles for a linear mapping are presented.Yayın On travelling wave solutions of a generalized Davey-Stewartson system(Oxford Univ Press, 2005-02) Eden, Osman Alp; Erbay, SaadetThe generalized Davey-Stewartson (GDS) equations, as derived by Babaoglu & Erbay (2004, Int. J. Non-Linear Mech., 39, 941-949), is a system of three coupled equations in (2 + 1) dimensions modelling wave propagation in an infinite elastic medium. The physical parameters (gamma, m(1), m(2), lambda and n) of the system allow one to classify the equations as elliptic-elliptic-elliptic (EEE), elliptic-elliptic-hyperbolic (EEH), elliptic-hyperbolic-hyperbolic (EHH), hyperbolic-elliptic-elliptic (HEE), hyperbolic-hyperbolic-hyperbolic (HHH) and hyperbolic-elliptic-hyperbolic (HEH) (Babaoglu et al., 2004, preprint). In this note, we only consider the EEE and HEE cases and seek travelling wave solutions to GDS systems. By deriving Pohozaev-type identities we establish some necessary conditions on the parameters for the existence of travelling waves, when solutions satisfy some integrability conditions. Using the explicit solutions given in Babaoglu & Erbay (2004) we also show that the parameter constraints must be weaker in the absence of such integrability conditions.Yayın Two reflector non symmetric shaped antenna systems(IEEE, 2000) Hasanoğlu, ElmanTwo reflector antenna systems with non symmetric reflecting surfaces under GO approximation are investigated. It is shown, that the problem of forming desired far field pattern leades to solving the system of partial differential equations with respect to mapping functions between wave fronts. One of these equations is non linear and expresses energy conversation law. It is shown that this equation can be solved separetly in the class of non smooth functions which has a discontinuty of first kind along a given curve.Yayın A numerical study of the long wave-short wave interaction equations(Elsevier B.V., 2007-03-07) Borluk, Handan; Muslu, Gülçin Mihriye; Erbay, Hüsnü AtaTwo numerical methods are presented for the periodic initial-value problem of the long wave-short wave interaction equations describing the interaction between one long longitudinal wave and two short transverse waves propagating in a generalized elastic medium. The first one is the relaxation method, which is implicit with second-order accuracy in both space and time. The second one is the split-step Fourier method, which is of spectral-order accuracy in space. We consider the first-, second- and fourth-order versions of the split-step method, which are first-, second- and fourth-order accurate in time, respectively. The present split-step method profits from the existence of a simple analytical solution for the nonlinear subproblem. We numerically test both the relaxation method and the split-step schemes for a problem concerning the motion of a single solitary wave. We compare the accuracies of the split-step schemes with that of the relaxation method. Assessments of the efficiency of the schemes show that the fourth-order split-step Fourier scheme is the most efficient among the numerical schemes considered.Yayın A note on the wave propagation in water of variable depth(Elsevier Science Inc, 2011-11-01) Demiray, HilmiIn the present work, utilizing the two dimensional equations of an incompressible inviscid fluid and the reductive perturbation method we studied the propagation of weakly nonlinear waves in water of variable depth. For the case of slowly varying depth, the evolution equation is obtained as the variable coefficient Korteweg-de Vries (KdV) equation. Due to the difficulties for the analytical solutions, a numerical technics so called "the method of integrating factor" is used and the evolution equation is solved under a given initial condition and the bottom topography. It is observed the parameters of bottom topography causes to the changes in wave amplitude, wave profile and the wave speed.Yayın Influence of the velocity on the energy patterns of moving scatterers(Taylor & Francis, 2004) İdemen, Mehmet Mithat; Alkumru, AliParallel to the developments in the communication through space vehicles achieved during the last two decades, the scattering problems connected with moving objects became more and more important from both theoretical and practical points of view. Same problems are also arisen in point of space science, radio astronomy, radar techniques and particle physics. The earlier investigations available in the open literature concern the analysis of the scattered field pattern and, hence, treat the polarization, frequency shift (Doppler effect), aberration, etc, which are all important from both pure scientific and technological points of view. But, another issue which is also important in regard to the communication, antennas and particle physics is the influence of the motion on the scattered energy patterns which involves the radar cross-section and scattering coefficient. This paper is devoted to this purpose and aims to study the influence of the velocity on the received and scattered energies. Notice that the scattered wave is not time-harmonic even though the incident wave is so because the Lorentz transformation formulas interrelate the space coordinates and time, which makes impossible to extend the notion of radar cross-section to moving bodies. For the sake of simplicity of the mathematical manipulations, only two-dimensional case is taken into account but the method can be adapted by straightforward extensions to other types of scatterer.Yayın 3-D Vibration analysis of the rectangular micro damaged plates(Springer, 2008) Kiriş, Ahmet; İnan, EsinIn the present work, damaged plates are modeled by the micro-elongation theory which neglects the micropolar effects in Eringen's microstretch theory. The wave propagation problem is Studied and a new wave which does not appear in the classical theory of elasticity is observed. The Ritz method is extended to the microelongation theory and triplicate Chebyshev series multiplied by a boundary function are used as admissible functions to approximate plate deflection, and the frequency equations of the microelongated plate are obtained by using Chebyshev-Ritz method. The additional frequencies due to the microstructure of the plate are observed among the values of the classical frequencies. We examined the relation between these additional frequencies and the material constants of the microelongated medium and observed that these additional frequencies disappear while the all microelongational constants are taken as zero.
