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Scopus Q: Q3 × Konu: Solitary waves ×

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Listeleniyor 1 - 5 / 5
  • Küçük Resim
    Yayın
    Interactions of nonlinear waves in fluid-filled elastic tubes
    (Verlag Z Naturforsch, 2007-02) Demiray, Hilmi
    In 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.
  • Küçük Resim
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    An analysis of higher order terms for ion-acoustic waves by use of the modified Poincar,-Lighthill-Kuo method
    (Springer India, 2015-10) Demiray, Hilmi
    In 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.
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    Harmonic resonance phenomena on nonlinear SH waves
    (Işık University Press, 2023-04) Ahmetolan, Semra; Özdemir, Neşe; Peker Dobie, Ayşe; Demirci, Ali
    The interaction of shear horizontal (SH) waves in a two layered elastic medium and its mth harmonic component is studied. The dispersion relation is analysed to obtain the wave number-phase velocity pairs where the third and fifth harmonic resonance phenomena emerge. By employing an asymptotic perturbation method it is shown that the balance between the weak nonlinearity and dispersion yields a coupled nonlinear Schrödinger (CNLS) equation for the slowly varying amplitudes of the fundamental wave and its fifth harmonic component. The nonlinearity effects of the materials and the ratio of layers’ thicknesses on the linear instabilities of solutions and the existence of solitary waves are examined.
  • Küçük Resim
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    Propagation of weakly nonlinear waves in fluid-filled thick viscoelastic tubes
    (Elsevier Science Inc., 1999-10) Demiray, Hilmi
    In the present work, we studied the propagation of small-but-finite-amplitude waves in a prestressed thick walled viscoelastic tube filled with an incompressible inviscid fluid. In order to include the dispersion, the wall's inertial and shear effects are taken into account in determining the inner pressure-inner cross-sectional area relation. Using the reductive perturbation method, the propagation of weakly nonlinear waves in the long-wave approximation is investigated. After obtaining the general evolution equation in the long-wave approximation, by a proper scaling, it is shown that this general equation reduces to the well-known evolution equations such as the Burgers, Korteweg-de Vries (KdV), Koteweg-de Vries-Burgers (KdVB) and the generalized Burgers' equations. By proper re-scaling of the perturbation parameter, the modified form of the evolution equations is also obtained. The variations of the travelling wave profile with initial deformation and the viscosity coefficients are numerically evaluated and the results are illustrated in some figures.
  • Küçük Resim
    Yayın
    The modified reductive perturbation method as applied to the Boussinesq equation
    (Verlag Z Naturforsch, 2007-08) Demiray, Hilmi
    In this work, we extended the application of "the modified reductive perturbation method" to long water waves and obtained the governing equations of Korteweg-de Vries (KdV) hierarchy. Seeking localized travelling wave solutions to these evolution equations we have determined the scale parameter g, so as to remove the possible secularities that might occur. To indicate the effectiveness and the elegance of the present method, we studied the problem of the "dressed solitary wave method" and obtained exactly the same result. The present method seems to be fairly simple and practical as compared to the renormalization method and the multiple scale expansion method existing in the current literature.