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Bölüm: Işık University, Faculty of Arts and Sciences, Department of Mathematics × Tam Metin: false ×

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  • Küçük Resim Yok
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    Variable coefficient Korteweg-deVries equation in fluid-filled elastic tubes
    (Technical University Liberec, 2011-09-05) Demiray, Hilmi
    In 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.
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    On extensions, Lie-Poisson systems, and dissipation
    (Heldermann Verlag, 2022-07-06) Esen, Oğul; Özcan, Gökhan; Sütlü, Serkan
    Lie-Poisson systems on the dual spaces of unified products are studied. Having been equipped with a twisted 2-cocycle term, the extending structure framework allows not only to study the dynamics on 2-cocycle extensions, but also to (de)couple mutually interacting Lie-Poisson systems. On the other hand, symmetric brackets; such as the double bracket, the Cartan-Killing bracket, the Casimir dissipation bracket, and the Hamilton dissipation bracket are worked out in detail. Accordingly, the collective motion of two mutually interacting irreversible dynamics, as well as the mutually interacting metriplectic flows, are obtained. The theoretical results are illustrated in three examples. As an infinite-dimensional physical model, decompositions of the BBGKY hierarchy are presented. As for the finite-dimensional examples, the coupling of two Heisenberg algebras, and the coupling of two copies of 3D dynamics are studied.
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    Discrete dynamical systems over double cross-product Lie groupoids
    (World Scientific, 2021-03) Esen, Oğul; Sütlü, Serkan
    Discrete Euler-Lagrange equations are studied over double cross product Lie groupoids. As such, a geometric framework for the local analysis of a discrete dynamical system is established. The arguments are elucidated on the local discrete dynamics of a gauge groupoid. The discrete Elroy's beanie is studied as a physical example.
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    Exact solution of perturbed Kdv equation with variable dissipation coefficient
    (Ministry Communicatios & High Technologies Republic Azerbaijan, 2017) Demiray, Hilmi
    In 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.