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Variable coefficient modified KdV equation in fluid-filled elastic tubes with stenosis: Solitary waves

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  • Demiray, Hilmi

Abstract

In the present work, treating the arteries as a thin walled prestressed elastic tube with variable radius, and using the longwave approximation, we have studied the propagation of weakly nonlinear waves in such a fluid-filled elastic tube, by employing the reductive perturbation method. By considering the blood as an incompressible non-viscous fluid, the evolution equation is obtained as variable coefficients Korteweg–de Vries equation. Noticing that for a set of initial deformations, the coefficient characterizing the nonlinearity vanish, by re-scaling the stretched coordinates we obtained the variable coefficient modified KdV equation. Progressive wave solution is sought for this evolution equation and it is found that the speed of the wave is variable along the tube axis.

Suggested Citation

  • Demiray, Hilmi, 2009. "Variable coefficient modified KdV equation in fluid-filled elastic tubes with stenosis: Solitary waves," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 358-364.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:1:p:358-364
    DOI: 10.1016/j.chaos.2008.12.014
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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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