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Forced KdV equation in a fluid-filled elastic tube with variable initial stretches

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  • Demiray, Hilmi

Abstract

In this work, by utilizing the nonlinear equations of motion of an incompressible, isotropic thin elastic tube subjected to a variable initial stretches both in the axial and the radial directions and the approximate equations of motion of an incompressible inviscid fluid, which is assumed to be a model for blood, we have studied the propagation of nonlinear waves in such a medium under the assumption of long wave approximation. Employing the reductive perturbation method we obtained the variable coefficient forced KdV equation as the evolution equation. By use of proper transformations for the dependent field and independent coordinate variables, we have shown that this evolution equation reduces to the conventional KdV equation, which admits the progressive wave solution. The numerical results reveal that the wave speed is variable in the axial coordinate and it decreases for increasing circumferential stretch (or radius). Such a result seems to be plausible from physical considerations. We further observed that, the wave amplitude gets smaller and smaller with increasing time parameter along the tube axis.

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  • Demiray, Hilmi, 2009. "Forced KdV equation in a fluid-filled elastic tube with variable initial stretches," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1388-1395.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:3:p:1388-1395
    DOI: 10.1016/j.chaos.2009.03.067
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    References listed on IDEAS

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    1. Gaik, Tay Kim & Demiray, Hilmi, 2008. "Forced Korteweg-de Vries–Burgers equation in an elastic tube filled with a variable viscosity fluid," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1134-1145.
    2. Demiray, Hilmi, 2008. "Weakly nonlinear waves in a fluid with variable viscosity contained in a prestressed thin elastic tube," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 196-202.
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