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Yayın Interactions of nonlinear waves in fluid-filled elastic tubes(Verlag Z Naturforsch, 2007-02) Demiray, HilmiIn this work, treating an artery as a prestressed thin-walled elastic tube and the blood as an inviscid fluid, the interactions of two nonlinear waves propagating in opposite directions are studied in the longwave approximation by use of the extended PLK (Poincare-Lighthill-Kuo) perturbation method. The results show that up to O(k(3)), where k is the wave number, the head-on collision of two solitary waves is elastic and the solitary waves preserve their original properties after the interaction. The leading-order analytical phase shifts and the trajectories of two solitons after the collision are derived explicitly.Yayın An analysis of higher order terms for ion-acoustic waves by use of the modified Poincar,-Lighthill-Kuo method(Springer India, 2015-10) Demiray, HilmiIn this work, by utilizing the modified Poincar,-Lighthill-Kuo (PLK) method, we studied the propagation of weakly nonlinear waves in a collisionless cold plasma 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 those of the modified reductive perturbation and re-normalization methods. The method presented here is quite simple and based on introducing a new set of stretched coordinates.
