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Head-on-collision of nonlinear waves in a fluid of variable viscosity contained in an elastic tube

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  • Demiray, Hilmi

Abstract

In this work, treating the arteries as a thin walled, prestressed elastic tube and the blood as an incompressible viscous fluid of variable viscosity, we have studied the interactions of two nonlinear waves, in the long wave approximation, through the use of extended PLK perturbation method, and the evolution equations are shown to be the Korteweg-deVries–Burgers equation. The results show that, up to O(ϵ3/2), the head-on-collision of two nonlinear progressive waves is elastic and the nonlinear progressive waves preserve their original properties after the collision. The phase functions for each wave are derived explicitly and it is shown that they are not straight lines anymore, they are rather some curves.

Suggested Citation

  • Demiray, Hilmi, 2009. "Head-on-collision of nonlinear waves in a fluid of variable viscosity contained in an elastic tube," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1578-1586.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:4:p:1578-1586
    DOI: 10.1016/j.chaos.2008.06.022
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    References listed on IDEAS

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    1. Demiray, Hilmi, 2006. "Interaction of nonlinear waves governed by Boussinesq equation," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1185-1189.
    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.
    3. Ramos, J.I., 2007. "Solitary wave interactions of the GRLW equation," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 479-491.
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