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Yayın Variable coefficient Korteweg-deVries equation in fluid-filled elastic tubes(Technical University Liberec, 2011-09-05) Demiray, HilmiIn the present work, treating the arteries as a prestressed thin elastic tube with a stenosis and the blood as an inviscid fluid, we have studied the propagation of weakly nonlinear waves in such a medium by use of the reductive perturbation method and obtained the variable coefficient Korteweg-deVries (KdV) equation as the evolution equation. A progressive wave type of solution to this evolution equation, in the sense of distribution, is presented and the result is discussed.Yayın Exact solution of perturbed Kdv equation with variable dissipation coefficient(Ministry Communicatios & High Technologies Republic Azerbaijan, 2017) Demiray, HilmiIn the present work we study the integrability condition for a variable coefficient Korteweg-deVries(KdV) equation. For that purpose, we first introduce some proper transformations for dependent and independent variables in such a way that the variable coefficient KdV equation reduces to the perturbed KdV equation with variable dissipation coefficient. Then, we apply the homogeneous balance (HB) method to this perturbed KdV equation to examine the integrability condition for this equation. The analysis reveals that if the dissipation coefficient function has a special structure the variable coefficient KdV equation is integrable. The progressive wave solution of evolution equation shows that the solution is unbounded and the wave amplitude decreases with time, which is to be expected from physical considerations.
