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Yayın Coupled quintic nonlinear Schrodinger equations in a generalized elastic solid(IOP Publishing Ltd, 2004-10-08) Hacınlıyan, Irma; Erbay, SaadetIn the present study, the nonlinear modulation of transverse waves propagating in a cubically nonlinear dispersive elastic medium is studied using a multiscale expansion of wave solutions. It is found that the propagation of quasimonochromatic transverse waves is described by a pair of coupled nonlinear Schrodinger (CNLS) equations. In the process of deriving the amplitude equations, it is observed that for a specific choice of material constants and wavenumber, the coefficient of nonlinear terms becomes zero, and the CNLS equations are no longer valid for describing the behaviour of transverse waves. In order to balance the nonlinear effects with the dispersive effects, by intensifying the nonlinearity, a new perturbation expansion is used near the critical wavenumber. It is found that the long time behaviour of the transverse waves about the critical wavenumber is given by a pair of coupled quintic nonlinear Schrodinger (CQNLS) equations. In the absence of one of the transverse waves, the CQNLS equations reduce to the single quintic nonlinear Schrodinger (QNLS) equation which has already been obtained in the context of water waves. By using a modified form of the so-called tanh method, some travelling wave solutions of the CQNLS equations are presented.Yayın Çok katmanlı düzlemsel ortam için termoakustik dalga denkleminin çözümü(IEEE, 2017-06-27) Bayıntır, Hazel; Ünalmış Uzun, Banu; İdemen, Mehmet Mithat; Karaman, MustafaBu çalışmada, farklı akustik parametrelere sahip çok katmanlı düzlemsel ortam için tüm katmanlarda kaynak dağılımı olduğu varsayımı altında termoakustik dalga denkleminin analitik olarak düz ve ters çözümü elde edilmiştir. Çok katmanlı düzlemsel ortam için elde edilen analitik çözüm katmanlı düzlemsel green fonksiyonlarına dayanmaktadır. Çok katmanlı düzlemsel modelleme meme, deri ve karın bölgesi görüntülemelerine uygun bir modellemedir. Elde edilen analitik çözüm ile literatürde var olan homojen ortam varsayımına dayanan çözüm her katmanda noktasal kaynak alınarak sayısal olarak karşılaştırılmıştır.Yayın A higher-order model for transverse waves in a generalized elastic solid(Pergamon-Elsevier Science, 2002-11) Hacınlıyan, Avadis Simon; Erbay, SaadetIn the present study, the nonlinear modulation of transverse waves propagating in a generalized elastic solid is studied using a multi-scale expansion of quasi-monochromatic wave solutions. In particular, to include the higher-order nonlinear and dispersive effects in the evolution equations, higher-order perturbation equations are considered, and it is shown that the modulation of two transverse waves is governed by a pair of the coupled higher-order nonlinear Schrodinger (HONLS) equations. In the absence of one of the transverse waves, the coupled HONLS equations reduce to the single HONLS equation that has already been obtained in the context of nonlinear optics. Some special solutions to the coupled HONLS equations are also presented.Yayın Two-dimensional wave packets in an elastic solid with couple stresses(Pergamon-Elsevier Science Ltd, 2004-08) Babaoğlu, Ceni; Erbay, SaadetThe problem of (2+1) (two spatial and one temporal) dimensional wave propagation in a bulk medium composed of an elastic material with couple stresses is considered. The aim is to derive (2+1) non-linear model equations for the description of elastic waves in the far field. Using a multi-scale expansion of quasi-monochromatic wave solutions, it is shown that the modulation of waves is governed by a system of three non-linear evolution equations. These equations involve amplitudes of a short transverse wave, a long transverse wave and a long longitudinal wave, and will be called the "generalized Davey Stewartson equations". Under some restrictions on parameter values, the generalized Davey-Stewartson equations reduce to the Davey-Stewartson and to the non-linear Schrodinger equations. Finally, some special solutions involving sech-tanh-tanh and tanh-tanh-tanh type solitary wave solutions are presented.Yayın Cross-sectional thermoacoustic imaging using multi-layer cylindrical media(IEEE, 2017-11-10) Elmas, Demet; Ünalmış Uzun, Banu; İdemen, Mehmet Mithat; Karaman, MustafaFor cross-sectional two-dimensional thermoacustic imaging of breast and brain, we explored solution of the wave equation using layered tissue model consisting of concentric annular layers on a cylindrical cross-section. To obtain the forward and inverse solutions of the thermoacoustic wave equation, we derived the Green's function involving Bessel and Hankel functions by employing the geometrical and acoustic parameters (densities and velocities) of layered media together with temporal initial condition, radiation conditions and continuity conditions on the layers' boundaries. The image reconstruction based on this approach involves the layer parameters as the apriori information which can be estimated from the acquired thermoacoustic data. To test and compare our layered solution with conventional solution based on homogeneous medium assumption, we performed simulations using numerical test phantoms consisting of sources distributed in the layered structure.
