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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 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 Weakly non-linear waves in a tapered elastic tube filled with an inviscid fluid(Pergamon-Elsevier Science Ltd, 2005-07) Bakırtaş, İlkay; Demiray, HilmiIn the present work, treating the artery as a tapered, thin walled, long and circularly conical prestressed elastic tube and using the longwave approximation, we have studied the propagation of weakly non-linear waves in such a fluid-filled elastic tube by employing the reductive perturbation method. By considering the blood as an incompressible inviscid fluid, the evolution equation is obtained as the Korteweg-de Vries equation with a variable coefficient. It is shown that this type of equation admits a solitary wave-type solution with variable wave speed. It is observed that, the wave speed decreases with distance for positive tapering while it increases for negative tapering. It is further observed that, the progressive wave profile for expanding tubes (a > 0) becomes more steepened whereas for narrowing tubes (a < 0) it becomes more flattened.Yayın Head-on collision of solitary waves in fluid-filled elastic tubes(Pergamon-Elsevier Science Ltd, 2005-08) Demiray, HilmiIn this work, treating the arteries as a thin walled, prestressed thin elastic tube and the blood as an inviscid fluid, we have studied the propagation of nonlinear waves, in the longwave approximation, through the use of extended PLK perturbation method. The results show that, up to O(epsilon(2)), the head-on collision of two solitary waves is elastic and the solitary waves preserve their original properties after the collision. The leading-order analytical phase shifts and the trajectories of two solitons after the collision are derived explicitly.Yayın The effect of a bump on wave propagation in a fluid-filled elastic tube(Pergamon-Elsevier Science Ltd., 2004-01) Demiray, HilmiIn the present work, treating the arteries as a thin walled prestressed elastic tube with variable cross-section, and using the longwave approximation, we have studied the propagation of weakly nonlinear waves in such a fluid-filled elastic tube by employing the reductive perturbation method. By considering the blood as an incompressible viscous fluid the evolution equation is obtained as the perturbed Korteweg-de Vries equation with variable coefficients. It is shown that this type of equations admit a solitary wave type of solution with variable wave speed. It is observed that, the wave speed gets smaller and smaller as we go away from the center of the bump. The wave speed reaches to its maximum value at the center of the bump.
